That's not really a choice for the visiting team to make. A team can only have two goalies dressed for a game. The emergency backup goalie rule (which is unique to the NHL, AFAIK) is that the home team has to have an emergency goalie booked who's available as a stand-in for either team should both of the team's dressed goalies get injured during the game. Either team would only realistically take that option if they have no other choice.

It's a relatively rare occurrence, and I imagine that anybody who ends up playing as an emergency backup would make an honest effort out of sportsmanship, and also because it's an unique opportunity and experience, even if it's for the visiting team.

The emergency backup goalie is essentially the ultimate underdog and ends up being the fan favourite for the game. Sometimes the home crowd has started to cheer for him even though he was playing for the visiting team.

I don't know what would be going through the emergency goalie's head if they had to step in for a really high-stakes game, though. I don't think that has happened so far.