From what I understand of the holodeck, sentient beings cannot leave it because they are sentient. If a robotic body (like Data's perhaps) could be manufactured and the program downloaded into this body, would it be possible to transport holographic beings from the holodeck? (Note - I am aware of the mobile emitter, but that is another 5 centuries away from TNG era, which is what I'm talking about).
Thanks to the episode Ship in a Bottle we know that it is possible to remove the program for a sentient computer program from a holodeck and run it in an external processing unit.
The real problem would be that no sophisticated android bodies exist in the Federation, during the time of The Next Generation, outside the seven Soong-type androids. Of those: three are damaged, destroyed or inoperable, two are already occupied and two are unaccounted for.
Therefore, yes, if you could find a suitable body that the program was willing to inhabit (or could be tricked into), then it would be possible to take a sentient program off the holodeck and into the real world.
This actually happens (sort of) in VOY 6x17, Spirit Folk.
One of the residents of the Fair Haven holodeck program is examining the Doctor's mobile emitter, when Tuvok gets a transporter lock and beams it off the holodeck. Instead of getting the Doctor, they get that character.
Granted, it being the mobile emitter, he could have just walked off of the holodeck, if he could find/summon the exit.