Supersonic ammo will work fine, but obviously won't be as quiet as subsonic ammo would be. The suppressor will take care of the muzzle blast, but won't change anything about the supersonic crack of the bullet.
I'm not positive about the accuracy or velocity drawbacks, but to the best of my knowledge, the only major problems you have are with wiped suppressors (mainly pistols) which have a neopreme disk that is hit by the bullet as it exits the suppressor. As long as you avoid those (and I don't know of a single high quality wiped rifle suppressor out there) you shouldn't have any problems.