Quite a few of the companies we've funded have already raised some money. It's not a problem if you raise money on a convertible note that YC's investment does

Quite a few of the companies we've funded have already raised some money. It's not a problem if you raise money on a convertible note that YC's investment doesn't trigger. You'd certainly need to incorporate and get a lawyer. Whether it would be worth the cost and distraction depends on the amount being invested, and the terms.