Probably, but even more importantly:

Make sure you reduce the credit limit on those existing BofA cards (at least a few days) before you close them.

Credit limit that's reduced while the card is still open is made available to new applications within a few months.

But credit limit which remains on a BofA card after it's closed is "tied up" for over a year !

So if you haven't done that already, start by reducing the credit limit as much as you can on the cards you're likely to close, while waiting to see if you get more input about how many you should close.