I can and have done this kind of stuff. In fact, I'm supposed to fix/finish Conical Johnson's bass.
I have an ambient microtonal ambient project, Burnt Infant, which just released an entire album of music done on a Hello Kitty stratocaster that I modified for quarter tones.
I'm going to both agree and disagree with the above posters. Fretless will not give you the kind of precision that a microtonal bass with frets will, if you are attempting chords. I'm sure it may be possible to play all those intervals on a fretless, but as our western ear isn't used to hearing them you're going have a very hard time. I will also say that playing microtonal instruments lose a lot of their intrinsic coolness if you aren't playing chords - bass is primarily a one note at a time affair, and I can't imagine playing microtonal intervals one note at a time to be terribly exciting - it will just sound like you're out of tune. Also, it is more difficult to determine the subtleties of pitch the lower you go in the scale, so a microtonal bass won't sound nearly as exotic as a guitar would.
If you're going to do something like that, experiment with something cheap first.