Okay, that's a tough one. I would say the limiting factor is probably the state of your finger tendons; climbing puts a lot of stress on them, and climbers spend much time in arcane rituals to ward off tendon and pulley injuries. So yeah, that doesn't sound promising.

OTOH, my uneducated impression (based on my own attempts to ward off elbow tendonitis) is that tendon problems are often highly specific, and climbing works muscles and tendons in ways that are quite different from everyday movements.

So it's possible that issues that are badly aggravated by typing (for example) may be relatively okay with the gripping movements in climbing.