Do astronauts print 3D in space with supports? They are needed only because of gravity, which - on a space station - obviously is not a problem.
Supports are not needed "just" because of gravity. They hold pieces in exact position relative to the "bed" (and so relative to the coordinate system).
With most printers the model moves during print in at least one position, whether Y or Z, and if you just suspended some pieces in midair when they are not connected to the main body during print, they would just stay in space relative to the printer main body/station, so they would effectively move against the rest of the print and ruin your day.
On the other hand "suspending" layers without any support would probably not be possible anyway, because they would stick to your nozzle (for FDM, but imho most other technologies have some similar problem).
I have no links to validate this answer, but with a few years of 3D printing behind me, I can attest to the effect of gravity on 3D printing.
Micro-gravity would be a boon for earth-bound 3D printing enthusiasts. There would be no droop to the filament when bridging (spanning open areas) and no fallen models without support. The construction of each layer would be dependent on the bond to the previous layer which is how it's done on the planet, but there would be no outside force (is gravity an outside force?) causing the new layer to fall. There would be no fall, so to speak, because the entire model being printed is falling around the earth at the same rate.
There are 3D printers described as five-axis printers which rotate the model in three-space to direct the filament "downward" respective to the desired placement, but it's not really artificial gravity.
Zero-G would enable some creativity that is unavailable to mere mortals. Loops of filament could be extruded without sag, allowing for intricate latticework and rather stunning artistic creation.