In theory yes, at the end of overtime, if both teams continued to take penalties, and no one ever scored, the game could go on indefinitely (just like the playoffs). It seems like this would be rare as someone would be likely to score in 3-on-3 or 4-on-3 or 5-on-3 situations, and there's little incentive to take a penalty when you're on minute 6 of overtime and you're on a powerplay.
If this was a concern it could quite easily be remedied by hard-capping the overtime period (for example: time could be extended, but by no more than 5 minutes).
But that's already what overtime is. If you extend it another 5 minutes then eventually you run into the exact same problem, because you're not actually changing anything.
If a player is still in the box for a penalty at the end of the overtime period, that player should not be allowed to participate in the shootout. Barring that, I see no way that you could implement any real consequences, given that you run the risk of more penalties being called in the duration of extended play.