You can monitor incoming traffic to your system, even if it doesn’t get to the application it was aimed at.
Bittorrent traffic comes from other computers just like yours, owned by people just like you, with connections just like yours. When you stop your client, there is no process or procedure or central control that can instantly tell all those other people to stop sending to you. A peer continues to try to do just that.
The peer sends a packet, then waits for an acknowledgment (which you never send now). The peer waits, then tries again. This continues for a few more tries, then the peer decides you’re not going to respond, so it stops sending. The process doesn’t take that long, just a few minutes.
Meantime, another peer is looking for other connections. It consults the list that it got from the tracker a few minutes before you decided to quit. Its list says you’re interested in this torrent, so that peer now tries to contact you. It sends packets to you, but you don’t respond. It too eventually gives up. Repeat many times.
Every peer out there must obtain an updated list from the tracker, one that doesn’t have you on it, before the last of the incoming traffic actually dies out. That can take an hour, or even more before the last of it stops. Most of the traffic stops quickly, but it’s going to continue to trickle in for a long time. Whether you “pause” or “stop”, the system behaves exactly the same.
That doesn’t significantly affect your bandwidth. It doesn’t affect your upstream bandwidth at all. We know this because this is how the bittorrent protocol works. It’s not a mystery, it was designed and built this way.
As has been answered elsewhere, a browser can happily co=exist with BitComet provided you’ve configured BitComet for your system properly.