(1) it would be the same as saying that a folk tune will only survive if it can be hummed without the need for instrumentation
That's not far off true. Singable tunes from composed classical works have made it into the folk musician's repertoire, but you won't find that happening with Webern's String Quartets or Varese's Ionization (a piece written for percussion only...), for example, or even the bits of a Mozart Symphony that aren't specially tuneful.

(2)
Firstly, were they written to be accompanied or unaccompanied in the first place?
That's not my point - which was whether the song stands on its own without accompaniment. If it was "written to be accompanied" there's a chance, but not proof, that it won't become a folk song in the sense of having a life of its own.

Secondly, what kind of singers will be performing them in the future - from 45 years of going to folk clubs and festivals, I'd say that a greater percentage of singers perform accompanied in some way than otherwise?
They may well do, but I submit that songs that can't stand up without the original accompaniement/arrangement aren't the ones that will still be getting sung in 50 years time.

Thirdly, how will these songs be preserved for posterity?
I would suggest not in communities, by oral tradition, but on CDs and recordings.

For pop songs, yes, and they will become museum pieces. If a song can't exist without the recording studio resources that were used to produce it (48 tracks of MIDI sequenced patches, vocal effects, drum fills, girlie choruses etc.) how will it ever get performed? (as opposed to just having recordings reproduced)

In an age where variety is valued above homogeneity, the most versatile songs - those that can be presented in the greatest variety of ways by the greatest number of people and are most open to interpretation - are the ones that are most likely to survive.

Well, I completely agree with you there, but I also think it's the songs whose main strength is in the words and the melody that are most susceptible to such re-arrangement. You can take away the original arrangement, put a completely different one back, and it's still the same song. And of course you can take a song that was collected from an unaccompanied singer in 1906 and add an accompaniment to it and it works - I've been doing exactly that for the last 8 years!

Anahata