My experience of doing just this does not seem to tally with what other people say here.
The changeover was a couple of years ago or so. The modem didn't lose synch when the changeover happened.
Even before I put in the new username and password into the router, the graph of the connection showed a marked improvement in latency, slight improvement is speed and significant improvement in packet loss. The yellow spike in the graph went away.
There was no loss of connectivity, apart from when the router restarted after I put the new login in. And that was several hours after the transfer had gone through.
I can't see how the line could have been switched to a different port without any loss of connectivity, so I assume it stayed on the same port.