I went back and checked the game code, it turns out it counts it as completed even if you ran out of time, which was... an interesting choice. I probably was going to remove the time limit and forgot about it. There's also no way to play it again after beating it (which happens no matter what), which is a bit of an oversight. Anyway, it doesn't give stars or record a clear time, so other than the sequence itself and the preceding cutscene you wouldn't be missing out on anything.