Any repetitive stress on a joint can lead to acute problems such as tendonitis and other joint-tendon syndromes, as well as problems like arthritis down the pike. On the other hand, many people do gnarly things to their joints and do fine. It depends on how often, how long, how hard, how you rest the joint at other times, your genetics, your diet, your general level of health.... In other words, bending your finger like that, especially if you're doing it frequently, could lead to long-term problems, but it would be impossible to say whether it actually will in your case.
One rule (that should be common-sense but usually isn't) is that if your hand or finger starts to hurt, STOP and rest it for a couple of days. If it hurts again when you start playing again, you should look at what you're doing and see if you can do it differently.
If you are a serious musician and having serious problems, I'd suggest finding an occupational therapist, or a physician who specializes in physical medicine and rehabilitation (a/k/a PM&R, or Physiatry) -- if possible, one who has experience working with musicians. Hope that doesn't leave you more confused than you started!