Yes, you can bid when you don't have enough money.

If a guy costs 10M and you have 11M, you can bid until you win him or give up. Even if it causes you to have a negative balance.

You can even bid on multiple players, all of whom cost 10M, if you have only 11M. Even if the first auction win gives you a negative balance. You can keep bidding on the other players and cause your debt to grow.

What you can't do is place an initial bid on players when you have a negative balance. But as long as you had enough money to place that first bid, you can bid forever.