As long as you have a routing and account number, Square will deposit funds. Here's a help article with more information.

That said, I highly recommend keeping your business and personal accounts separate. It will save a TON of time when it comes to end of year accounting. Now that you have an EIN and an established account, there shouldn't be any issue with opening a new account with your bank. If your accounts are separate already, you should be able to convert the new account to a business account with no issues.