To emphasis a few key points
1) on a single ticket, you will not be charged if the arriving flight arrives and provides insufficient time to make the connection -- including stuck in immigration.
2) If this happens the arriving carrier is responsible to get you to your destination -- it does not have to be on UA
3) UA if not the arriving carrier may also be willing to help
4) Coming from the EU, you likely will be eligible for EU261 comp if the delay becomes long enough

Will you have checked bags?
Are you a US passport holder?