So technically it is possible that a game will literally never end for the rest of time. If the PP continues on and another penalty occurs before it lapses they would then need to play out the next penalty as well. This could go on forever.
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).
The problem comes down to this: In pretty much every sport in the world, if you commit an infraction early in the game, there is a consequence. In basketball if you're fouled while shooting, you get to shoot free throws. In hockey, if you're tripped your team gets a 2 minute powerplay to try and score.
But in almost all other sports, that consequence in enforced consistently throughout the game. Hockey is the one sport where we throw away that consequence at the most crucial and exciting time of the game. I can trip you in the first period and you get a full 2 minute powerplay, but if I trip you with 20 seconds left, it's only a 20 second powerplay.
Aside from the "fairness" of it, it would make overtime more exciting and decrease the odds of games going to shootouts.