Strange as it may seem, I believe so. If we examine: the long forms, changing sections, form structure of establishing themes, solos, theme illusion and recapitulation and reiteration of theme; they all seem to be inherent in the very best that prog has to offer. Look at Close To The Edge, Gates Of Delirium, Karn Evil 9, Dogs, Suppers Ready, The Colony Of Slippermen, Thick as A Brick. All of them have the many qualities of classical music that was created by the masters.
For an easy relaxing listen to exemplify my point; listen to Schubert's Unifinished Symphony. It's only two movements and the theme is stated up front in the melody early on and weaved in and out of the total 25 minutes combined of the two movements. The standard form of symphonic style was four movements, so because Franz Schubert only wrote the two movements before he died at 31 years old; it was simply titled Unfinished.
Some actually suspect it wrote only the two sections intentionally; but I disagree, as the recapitulation and reiteration of the theme in the first movemnt is eluded too, but never resurfaces with power, as was Schubert's style, in the last movement.
What say you on this topic of classical music and it's influence on classic prog?
PS - If you haven't ever listened to classical music, you owe it to yourself to at least check out Beethoven's 5th Symphony, Tchaikovsky's 4th Symphony, Mozart's 40th, Stravinsky's Rite Of Spring and Dvoraks New World Symphony. There are many many other fine works that you can dig into for yourself. Afterall, to know where Prog is going you should know where it came from.