I broke my finger a year ago, and even after surgery, pinning, and PT, I havent (yet) restored the level of finger picking I was at pre-break. Getting there slowly though. Pain much less (still there), range of motion needs work. While the bones have healed (poorly I may add), Nerve, tendon and muscle damage will keep me from getting back 100%.
I never stopped gigging throughout the entire time though. I restarted my decades old pick use, and got pretty decent quickly. And the slacker middle finger (the one that broke) is now (nearly a year later) getting better. Trying to focus nearly entirely on fingerstyle again. Still have some difficulty doing octaves and rapid strokes. My fingertips for months felt as though they had exposed nerve endings, and the joints that were broken sometimes felt like there was broken glass rattling around in there. Still dealing with swelling and stiffness but less pain than first couple months.
The picks (I now use one about 2 songs per gig) that I chose to use are a mix of Fender med, heavy and extra heavy. Sometime use the orange grippy ones (Dunlop?). The positive result of my injury is it caused me to get proficient again with picks!