Probably until afterwards. Many schools don't start reviewing until August, while the April scores come in mid-June. It's still good to get everything in, though, especially since transcripts have a nasty habit of getting lost.
I don't know how adcoms arrange review of the first applications they look at. Perhaps they start with whatever ones were submitted first since there will be a lot of submissions between now and when the April scores come out. Early never kept anyone out of the running!