Well, looks like we're both right and we're both wrong.
1) I just tested. Played my Switch down to 80% and plugged it into an iPad charger (5.1v @2.1A) using the USB cable that came with the Switch Pro controller for about an hour and kept playing. It's now at 97%. Case closed. It
can charge while playing with that input.
2) Where I was wrong: Thought it fishy with 15v on a USB input (never paid much attention to the "fast charging" specs or USB 3.1+) but it says right on the console 15V @ 2.6A. Edit: and the article I just linked to below doesn't use a very accurate testing method, but it can't be THAT far off, and it agrees with what you say about the amperage.
Either way, I was right to begin with. Even though it seems slow, you will increase your battery charge while playing with a simple 5v 2.1A powerbank/plug.
Edit: And An article that both proves you correct on the Amperage, and me correct that a 5v 2.1A charger will provide a bit more than it uses while undocked (<9watts ) (and... as if I needed an article since I just proved it for myself anyway):
http://www.anandtech.com/show/11181/a-look-at-nintendo-switch-power-consumption/2
@xile6
@Sumea