The economic updates on Monday only consider the current economic status (and not any open bids). Thus, if you are currently at - $200k but another team has a bid on your player for $300k (making your balance $100k) that is closing on Tuesday, you will still have to pay interest on the $200k.
And yes, you are supposed to get an email warning to clear up your finances. I actually received one a couple of weeks involving a situation similar to yours.