I would have to think it does. I've done this to try to ensure I reach my minimum number of starts in a H2H league, and a backup goalie entering partway through a game would count as a game played, even if he didn't play the entire game. Likewise, if a goalie is pulled partway through it's a game played.
If you go to your Team Log, you will be able to view the stats earned by player for your team while they were in your starting lineup. I can't prove this using my own team, but you may be able to on yours (or someone else's).