Unfortunately no, the bank may not accept the offer. The lender(s) involved have the final say on the selling price; not the seller.
The bank may accept the offer, flat out reject it, or give you a counter offer. The process of obtaining an accepted offer from the bank may be lengthy so be prepared to wait a few weeks for a response.
I encourage you to work with a real estate agent who is experienced in the short sale process so that he/she can advise you on the process and keep you informed.
Good luck to you!
Prudential Connecticut Realty