I have noticed it while running ~/bin/some_command. The ~ doesn't echo until I also type the /. It doesn't cause any misbehavior because there is no binding for ~/ but can be slightly surprising.
I find it odd that you would have commands in ~/bin but not have it be the highest priority in your PATH. I use ~/.local/bin, but would never type it because i wouldn't have bins that overlap shell commands and no other path would have priority.
Usually, it is. IIRC, this was when I was just setting up my environment on a new host, after I had populated ~/bin but before I restarted my shell to pick up PATH modifications.
I'd guess this is because it only works in ssh PTY sessions. So it would have no effect on tunneling or when piping arbitrary data through ssh to a non-interactive remote command (unless you use the -t switch to force PTY allocation even when stdin is not a TTY).