If the "Living Constitution" means decisions where general principles put forth in the Constitution lead to results which the ratifers might not have expected (for instance, gender equality decisions, protecting pornography under the free speech clause, Lawrence v. Texas) then, arguably yes.
See this classic article by Thomas West on Allan Bloom, where Bloom asserts in The Closing of the American Mind:
This is a regime founded by philosophers and their students. . . . Our story is the majestic and triumphant march of the principles of freedom and equality, giving meaning to all that we have done or are doing. There are almost no accidents; everything that happens among us is a consequence of one or both of our principles. . . . [T]he problem of nature [is] always present but always repressed in the reconstruction of man demanded by freedom and equality. (97)
America was founded on liberty and equality. And many of the modern moral changes in society, according to Bloom, directly relate to evolving notions of liberty and equality. In other words, court decisions and other policy changes, although not what the ratifers of the Constitution "expected," logically grow from the general principles the Founders put forth. Even Robert Bork has observed this: "Equality and liberty are of course, what America said it was about from the beginning." Slouching Towards Gomorrah, p. 56. He further notes that the sixties (which he LOATHES) represented, in some respect, "an expansion of certain American (and Western) ideals" and that this "deserves to be stressed because if modern developments are in the American grain, if they grow from our roots, as there is reason to believe they do, they will be much harder to reverse than it is comfortable to think." Id.
So arguably, insofar as this approach pays homage to both the text and the ideals that underlie the Constitution, it is a form of originalism (perhaps, we could call it original meaning idealism). Justice Souter's opinion in Lee v. Weisman, explicitly grounded the ideas of Jefferson and Madison, is a textbook example of such an approach. Money quote:
"[T]hose practices prove, at best, that the Framers simply did not share a common understanding of the Establishment Clause, and, at worst, that they, like other politicians, could raise constitutional ideals one day and turn their backs on them the next."
As Souter notes, James Madison engaged in exactly such reasoning. The same Congress that helped to give us the First Amendment also put in Congressional Chaplains. There was never a lawsuit, during the Founding era, to get rid of such Chaplains. And they remain today. Yet on the question of their ultimate constitutionality, Madison wrote:
Is the appointment of Chaplains to the two Houses of Congress consistent with the Constitution, and with the pure principle of religious freedom?
In strictness the answer on both points must be in the negative. The Constitution of the U. S. forbids everything like an establishment of a national religion. The law appointing Chaplains establishes a religious worship for the national representatives, to be performed by Ministers of religion, elected by a majority of them; and these are to be paid out of the national taxes. Does not this involve the principle of a national establishment, applicable to a provision for a religious worship for the Constituent as well as of the representative Body, approved by the majority, and conducted by Ministers of religion paid by the entire nation.
The establishment of the chaplainship to Congs is a palpable violation of equal rights, as well as of Constitutional principles: The tenets of the chaplains elected [by the majority] shut the door of worship agst the members whose creeds & consciences forbid a participation in that of the majority. To say nothing of other sects, this is the case with that of Roman Catholics & Quakers who have always had members in one or both of the Legislative branches. Could a Catholic clergyman ever hope to be appointed a Chaplain? To say that his religious principles are obnoxious or that his sect is small, is to lift the evil at once and exhibit in its naked deformity the doctrine that religious truth is to be tested by numbers. or that the major sects have a right to govern the minor.
Social conservatives, like Bork, can react in a number of different ways. One way is to try to "freeze" liberty and equality circa the understanding in 1789 (or when each relevant provision of the Constitution was ratified). But that begs the question as to whether this is the only proper way to interpret the Constitution (Bork certainly acts as though it is; Madison didn't seem to think so). The text of the document doesn't tell us how to interpret the document. And indeed, many of the so called "activist" decisions (the free speech cases are textbook examples) are entirely supported by the broad and general wording of certain provisions in the text.
Jack Balkin has termed Bork's "Original Intent" as "Original Expectation Originalism." In other words, it asks did the framers and ratifiers specifically expect (with a specific awareness) the text outlawed the specific government practice in question. Did the Framers and ratifiers of the First Amendment know they were outlawing Congressional Chaplains? And then they look at practice as almost dispositive.
This method has the effect of reading the individual rights in the Constitution in almost the narrowest sense possible (so it produces outcomes with which social conservatives agree).
One of the biggest problems with original expectation originalism (both leftists and conservative Harry V. Jaffa have pointed this out), is it is quite frankly impossible for this approach to take the moral high ground. The Constitution of 1789, according to this approach, is a pro-slavery document. The only way to make the original Constitution an anti-slavery document is to abstract ideals from it and read it through the lens of the Declaration of Independence (which is what Justice Thomas says he does). Robert Locke has an article that is noteworthy because it represents a social conservative being quite frank about what the original Constitution stood for when read through the lens, not of its ideals, but rather its compromises with those ideals:
Crucial facts about what America was founded on are deliberately hushed up by both liberals and conservatives and admitted only by the non-respectable Left and the non-respectable Right. Namely, that this country was founded upon conquest, slavery, sexism, and class rule. The Constitution, as originally written, holds that our ownership of this land by conquest is just, that Indians are savages, that blacks may be enslaved, that women have no fit role in government, and that the (little-remembered) restriction of suffrage to men of property by state governments is valid.
If this is what "Original Intent" means, then I and I hope most other folks, don't want any part of it. Thankfully, our Founders gave us their ideals which allow us to rise above their illiberal and indefensible compromises.
Finally, let me state that I don't necessarily fault our Founders as "evil" for allowing such compromises. Many of the practices -- slavery being the classic example -- were so deeply ingrained into our traditions and institutions that they would be practically impossible in 1789 to uproot, or at least to uproot without causing our society to go into convulsions like the French did.