Is it possible to sniff traffic of a remote network? (With admin access to router)

If you can login remotely, then there will be very little that you cannot do. Once you have a root shell, you can easily run tcpdump. You can read the local databases that supply encryption keys elsewhere. If within that shell, you are missing commands; you can write, or simply go find the commands you want. If you do manage to get in, there is probably a lot of bandwidth; and you might go unnoticed for a while as long as things continue to work.

However, most people will let the ISP setup the router that connects to the ISP; and that's not going to have the default password and let the world in. Verizon uses an enormous UUID for the encryption key (written on a sticker on the modem), etc. There will be misconfigured stuff out there, but it's not like it used to be (with end users going to Best Buy and (mis)configuring it himself).