Thinking about it a little more, I don't see why pausing the game should in itself a disqualifying factor. There's a punishment for that built in: more time added to the run.
Since it's easy to tell when the game is paused, I think it would be sufficient to say that run time equals in game time plus total time paused.
It is a punishment for full game runs, but not for individual level runs as they are judged on in-game time.
When pausing the game you hear no sound, so you could theoretically edit out all the time inbetween. Possibly also on transitions after levels, but there you can't do anything about it. At least this way you put some constraints to it.
It is especially important for ILs. Note we use ingame time there for convenience (to not have to time manually). And by pausing during the race you abuse this because it was just introduced for convenience sake and not to allow you taking a break during the run. What matters is still your real time performance.
Additionally ingame time appears to not correlate with real time on some platforms, so it only makes sense to use it as long as it is consistent. This can be guaranteed only with no pausing during the race from what I know.
