I guess you know the strict answer is YES. But if I was going to use it up quickly I probably wouldn't. Salsa isn't much different from the chutney recipe I just made. Chutney is said to be better if it "sits" for a month or so after canning. Is salsa the same?
Sterilizing takes very little time. I put my jars in the dishwasher timed to be just starting the dry cycle when I need them, I don't let them dry so that they are still freshly very hot. My dishwasher even has a sterilize cycle but a hot wash would be good enough. The lids, funnel and tongs simmer in a pot of boiling water while I stir the last minutes of the chutney. Everything is hot and ready to go all at once. I get such a kick out of hearing the lids snap as the vacuum effect of the hot chutney cooling in the cooling jars draws the lids down tight.