**tl;dr** It should be fine, if not necessarily comfortable. Depending on your budget and interest in roughing it, an airport hotel room would be a reasonable alternative.

From [Sleeping in Airports](https://www.sleepinginairports.net/guides/washington-reagan-airport-guide.htm) and specifically from their [Washingon Reagan Airport sleep guide](https://www.sleepinginairports.net/sleep-guide/sleeping-in-washington-reagan-airport.htm):

> While Washington Dulles Airport is technically open 24-hours, the Security checkpoints and Secure areas do close for the evening, likely by 11:00 PM. Even if you’re already inside Security, you may have to relocate to the pre-Secure area.

Since you asked in comments, that basically means you'll have to go out through the security checkpoints: you won't be able to stay "in the lounge where the plane lands".

> Most seating here is equipped with armrests, so don’t expect too much comfort. Maybe travellers report sleeping on the floor, particularly near the heat vents next to the windows. A sleep mat or sleeping bag will provide some much-needed cushion.

> Airport security don’t seem to mind overnight campers, as long as you stick to the pre-Security areas at night.

The site has more details about temperature (generally cold), brightness (generally bright), and other tips.