I had a short connection at MAD with separate tickets (1:45 connection), albeit IB to T4S from the US and another IB ticket internal to Spain with checked bags.

I landed at 2, had checked bags by 230 and made it through immigration and customs, and rechecked in for the new flight by 3. Of course, it helped that I was in J and there wasn't much of a line at immigration. You're not checking a bag so it would be easier, although you need to change terminals.