I'm trying to remember if _Accelerando_ eventually features FTL.
I think there's an episode where software copies of important
cast members are FTL-communicated to another star system.
Meanwhile their meat originals live and die off-stage, presumably
to say something about their loss of significance in the story
by this point, it being, eventually, the sort of story where
that's liable to happen.
_Schild's Ladder_ has speed of light limit in our physics, but
presents a means to create a universe with /different/ physics.
And, yeah, generation ships and coldsleep ships. And also stories
where FTL is discovered and there are missions to rescue the
people who are stuck on generation ships or in space iceboxes.
Consulting Neil R. Jones's _The Jameson Satellite_, at
<
http://www.gutenberg.org/files/26906/26906-h/26906-h.htm>
I see that the immortal machine-men go on voyages of hundreds
of years (presumably our years) but are from "millions of light
years distant", so they are using FTL after all, "at an
inconceivable speed". Well... inconceivable is the /opposite/
of imaginary, which you were asking about... imaginary is what
you can think about, but not do; inconceivable is what you can't
think about. So, all of the other stories where authors brush
aside the speed of light limit or don't mention it at all, and
aren't thinking about it, must be using inconceivable drive, no
imaginary drive.