Short-hauls into IAD during peak times are a mess because of ATC. They are the first to get delayed/cancelled.

To answer the specific question, if you misconnect at IAD due to something outside UA's control such as WX, ATC or even crew delay (presumably meaning the crew for your flight is delayed inbound from elsewhere, not that they're off at a bar and forget), you are on your own overnight.

As others suggest, I would have the other BOS-DAY options printed out and ready to go. If there's a problem, the more proactive you are about suggesting alternatives, the better off you are.