FDIC Insured limit $250k

FDIC insured limit per account is $250k, but it is okay to put more money in the account, correct? As long as you believe the bank will not go bankruptcy. 

I am thinking to transfer fund from brokerage account to a bank saving account for a few months, for the purpose of buying house. The money needs to stay at bank account for at least two statement cycle, then apply for pre-approval mortgage, then find a buyer agent. And the bank saving account balance will also be used for cashier check during house closing day.

I don't expect the money staying on the bank account for more than 6 months.

Thanks.