It sounds like your biz checking isn't local, so you need a way to deposit cash from where you live. Of course you can do it as you suggest. But is your remote bank connected to a local ATM network that would allow you to deposit it that way? You could also just deposit it to petty cash, keep the money in a safe place, and then spend it locally as necessary, using petty cash as your payment method. 

I would try to open a local biz checking acct, for just such a situation.

In other words, you have lots of options and you can do it the way that works for you best!