What's the harm?
Notwithstanding the removal of a lot of the bank managers' power, it can't hurt to keep one onside (or at least avoiding the possibility of having him/her offside by rejecting a LinkedIn request).
And perhaps banks are using LinkedIn to verify an applicant's bona fides?
I'm not saying that either of the above will necessarily happen, but I'm a great believer in risk management. There is no real risk in accepting the connection. There is a risk, however small, in not accepting the connection. Ergo, you should accept the connection.