Okay, here's the proof; papayas can be flowered from seed in the Washington area. Click on the picture to better see the flowers. Specifically in the Washington Youth Garden at the USNA. As to whether they can harvest ripe fruits....possibly not. The papayas in containers on the East Terrace of the Administration building had not flowered at my last check and they are bigger than my own container plants. Nonetheless all are performing excellently as bold foliage elements.
The Youth Garden plants have definitely been treated right; they are growing in a the ground in what looks to be a raised bed/berm of either pure compost or heavily enriched organic soil. I suspect they can grow fast enough to use any amount of water they get and they certainly aren't deprived! In the tropics the rule of thumb for fruiting is 5-8 months. We don't really have that much tropical weather here in DC, but it will be exciting to see how far the fruit can get.