Biotin?
Nothing is going to stop the hair from falling out if it's going to. Everyone reacts differently, but most people experience telogen effluvium to one degree or another after weight loss surgery. Biotin can help the hair that starts regrowing after falling out, but it's not going to do anything to keep it from falling out in the first place.
If you're one of the people affected strongly, my advice is to get a cute, short, layered haircut. Use volumizing products and blow dry to add a bit of fluffiness. See a good hairstylist for more ideas, but don't buy into a sales pitch for products that help regrow hair. Toppix hair fibers can help camouflage severe loss, or in serious cases wigs or hairpieces can help out. The best news is that for the vast majority of people the hair loss is not noticeable by others, and it's all temporary. Your hair will grow bac****ep thinking about how much healthier and happier you'll be; for most people who have WLS, it's a trade off they'd gladly make.
Good luck!
Surgery: RNY on 12/18/2013 with Jay M. Snow, MD "Don't mistake my kindness for weakness." - Robert Herjavec, quoting Al Capone
Most hair loss after surgery is due to something called telogen effluvium and if you mean does biotin prevent telogen effluvium, no, it doesn't. Biotin is one of the B vitamins. If you have a biotin deficiency, that can cause hair loss. Biotin deficiency is very rare, though. So unless you are losing hair due to an extremely rare biotin deficiency, taking biotin won't help.
Please note: I AM NOT A DOCTOR. If you want medical advice, talk to your doctor. Whatever I post, there is probably some surgeon or other health care provider somewhere that disagrees with me. If you want to know what your surgeon thinks, then ask him or her. Check out my blog.