Im planning to book a UA flight from GRU to IAD via IAH on both UA metal arriving 05:30H and leaving at 19:10H, roughly 13 hours and 40 minutes transit in IAH.

UA website says "United will transfer bags to a connecting flight when the connecting flight is scheduled to depart within 13 hours of the customer arriving at the connecting city. Customers making connections that involve an overnight stay must claim baggage and re-check baggage, subject to applicable charges, for the connecting flight on the following day"

So question is will they tag my bags all the way to IAD ? How about if they tellme that 13 hours and 40 minutes is not 13 hours at all? Do I have to beg?

If worse comes to worse, is there a left luggage facility at IAH? I know there are no lockers. THanks