From my experience, there are two ways people make starters:
1. Make the starter the day of to "wake" the yeast up
2. Make the starter 2-3 days before to grow yeast
Number 1 doesn't mean that you have enough viable yeast and you could still be underpitching. Fermentation just starts quicker because they have been munching ahead of time. However, depending on the strain, the yeast will begin to reproduce in as little as an hour or two. I have done number 1 in situations similar to yours, but I prefer to do number 2 and I have much better results because you have the proper pitching rates. That is the purpose of making a starter after all. It really only takes about 20 minutes for me to make a starter, so it's not that big of a deal. Your always free to do what works best for you, but I recommend making it a couple days ahead of time so you have the proper amount of yeast.