Well, it wouldn't be an instant by-election if some member didn't vote by the whip... unless they were expelled. If so, I suppose it could result in a by-election if some other party opportunistically said "Hey, come join us!!". If that member elected to sit as an independent then I would need no need for a by-election.
If that's the only rule, then the House basically plays its own version of the Liberal Senate game. "No, of [i]course[/i] they're not a member of our caucus! There's a huge difference between an NDP MP and an Independent NDPer!"