noip.c: Factor out the non-implicit-binding parts of `do_implicit_bind'.

The function's other responsibilities are taken over by a new function
`fixup_client_socket'.  When I did this, I anticipated that I was going
to have to make the latter rather more complicated, but it turns out
that it's not actually that far off.

No functional change, though the new function takes a different approach
to producing the same effective control flow.