It is possible to catch the 16:44 train. If the plane is on time, and the immigration lines are not packed up from a number of arrivals.

The train to Asakusa would basically be a standard commuter layout on board the train. As you get on at the start of the route, you would easily get seats, but there is basically no luggage storage, you'll kind of have to manage that in the potential crowds.

You could also make 16:59 Skyliner and change to the Ginza line to Asakusa at Ueno. Though the Ginza line access at Ueno is not exactly luggage friendly.