I think that would work fine as long as some of it gets used to buy some things with the debit card. The problem is withdrawing all the way back to a USD bank account. Spending on a Paypal debit card flies.
Paypal does not make money unless they collect the debit card fees from the merchant. Banks are not making any money in this scenario so, do not give them a a chance to whine if chunks go back and forth to Paypal.
I think banks make a lot of money on check/debit cards so they are going to be worried that Paypal is getting some of their action?