I activated a pack last Saturday night and didn't pitch it in until later in the day on Sunday. Brew has been fermenting just fine. You can leave it out in a cool room (within the yeast's posted temperature range would be fine)... Just sanitize the packet before you open and pitch. So, basically, business as usual.
You most definitely can use the yeast a while after it has been activated. All activation does is dump a little wort and nutrient into the yeast to kick start it. If you don't use it, it will just be dormant again. Not a big deal. Just do your starter like normal.