It isn't really possible to attempt to answer the question without enlarging a bit on the whole issue of the influence of mass media on the transmission of song in general, but there is no need for a definition of folk music here, nor was one asked for; the specific question can only be addressed by accepting, for the sake of the argument, Maud Karpeles' definition.  Anyone who doesn't know, or understand, what that was should probably consider remaining silent; there is little point in insisting on talking about cabbages when asked for directions to the station.

An Introduction to English Folk Song was first published in 1973, but represents a set of theories initiated largely by Cecil Sharp in his book English Folk Song: Some Conclusions.  This was first published in 1907, and Sharp made it clear at the time that these conclusions were provisional only, and he expected later scholarship to modify them considerably.  The last revision of the book (made by Maud Karpeles) was issued in 1954, and essentially her opinions on the fundamentals of the nature of traditional music seem to have been fully formed by then, though she was by no means so closed to new ideas as people who have not read her writings might suppose.

Maud Karpeles made a perfectly valid point, though it was certainly not the last word on the subject.  More recent scholarship would take a rather broader view, of course, but it is certainly the case that dissemination through mass media tends to distort tradition, at least in the short term, by promulgating "standard" versions which become widespread not necessarily through intrinsic worth, but because they are well-known.  We see examples of this here every day.  It is by no means a new phenomenon; the broadside press had a similar effect during the nineteenth century.  By comparison, the publishing of collected material by Sharp, Karpeles and the others, though very important, has had, in itself, a negligible impact.

A lot of work remains to be done in the study of this process, which is by no means fully understood even now, and there is material for a good few doctoral theses in the subject yet.  Particular work is needed on the mechanisms and contexts through which composed songs are assimilated and re-processed as "anonymous" pieces, often with fictional provenances attached, whether as described in Harvey's post or as in the many cases of songs of known authorship which have miraculously become "traditional Irish" in the imaginations of many.  Whether such pieces are really on the way to becoming genuinely traditional remains to be seen; it is not something that happens overnight.  The fact that one or more people believe a song to be traditional does not make it so.

Baldly to dismiss Miss Karpeles as "wrong", and her opinions as "rubbish", suggests a certain lack of understanding, coupled with not a little presumption; she knew far more about the subject, after all, than do any of us.  Her comments may well have been over-pessimistic, but it is too soon for a definitive answer.  At present, as Don said, the closest we can get to a sensible answer is a qualified (and provisional) "yes and no".

It is depressingly common for people who appear never to have read Sharp or Karpeles to attack them for opinions they did not hold, and for actions they did not take.  Neither of them, for example, believed or asserted that a song with a known composer could not become a folk song; indeed, Miss Karpeles' book contains several specific examples of the products of art-music being adopted into tradition.   She certainly felt that such songs were unlikely to become folk songs in the conditions of the early 1970s, but that is not the same thing.

We may feel that her views were over-cautious and conservative, but we have the benefit of nearly thirty years' hindsight, after all, and we should not presume to believe that we know what her opinions would be if she were alive today.