I've had plenty of injuries make their way through the hospital--no one has ever grabbed a crutch. I have had one patient in the hospital for going on ten years now, but everyone else made it out (or bled to death on the table) ok, some returning to the military and others back to regular life--and some as soldiers returning to civilian life due to all the red limbs and other parts. The one long-term patient, I removed the bed out from under her and she crawled into another bed. So she wasn't OK to leave. Everyone seems to take turns feeding her, and all the wounded parts have been yellow (initially red) for many years--her stats say she's incredibly slow to heal. I believe it--a hammerdwarf was on the flipside incredibly quick to heal and was out of bed in one season.
Often they heal to yellow and then an off yellow color and they function fairly normally.
if an infection isn't treated in time, the dwarf may die. Typically bears and dogs of mine will die of infection, if they can't grab a bar of soap in time I guess. The dwarf doctors will use soap when cleaning a patient if possible. Anyway it is sort of comical to see a dwarf with four sutures, four splints, and clothes wrapped around various body parts, making their way around the fortress.
I have also had dwarfs get up in the middle of surgery, go complete a few tasks, and go back to bed and get surgery again. If they keep that up they often get infected.
I had a farmer that grumbled every time there was a patrol duty and was angry to be drafted and he NEVER went up in combat skills beyond dabbling. Everyone else in the group progressed normally. Finally he got a foot injury and I relieved him of duty and he was happy to be farming and butchering, constantly aborting his surgeries only to come back after butchering a forgotten beast or two. I bet he wishes he still was armored during that one recent siege.. or he may still be with us today!
If your surgeons are endlessly cutting... that happened to me in .03, and seems to be fixed in .04. I haven't had any real issues in .04 that are worse than .03, and I never used the graphics so that wasn't an issue.
Lastly, and you didn't ask... try to keep your adamantine threads AWAY from the hospital, or they'll end up in sutures! Forbid them if you see them there, or keep them unforbidden and hope you get to make use of them before someone gets hurt...
I have found the medical process is much easier when dedicating a few dwarfs to overlap in medical skill sets, and have a few other skills enabled--I have a farm by the hospital, so I have the doctors farm. My chief medical dwarf became a legendary furnace operator, so he's never around (140 z levels down) when the action happens, but in case he does show up near the surface, he has the tasks enabled. I only let them haul when I think it's safe! Otherwise they end up picking up goblin loot on the other side of the map, left over from the last siege, just to get shot at by a troll ranger or goblin crowssbow wielder when the next siege happens.