No, because like shootouts it changes the very nature of the game. What if one
team has a goaltender standing on his head for 60 minutes, and his play is what
results in the game being tied? That team is obviously disadvantaged in OT if
there are suddenly no goaltenders.

If we absolutely must have a winner, I could see going to shootouts during
regular season play. But in any tournament situation infinite 20 minute OT's
until a goal is scored is the only way to go.