No, the bank has hedged everything. As soon as the bank issued your mortgage they sold a few bonds at the current interest rate, they collect your payments and pay off the bonds. The bond holders are betting that stay low, not the bank.

While in theory if rates go up you could find the bond for your house and buy it at a greatly reduced rate, thus paying much less for your house. In practice there is no individual bond for your house so you can't do this.