I agree with the above poster. Basic is actually a fairly strong herb, and a little goes a long way. There are many astrigent compounds in basil that don't come across in the aroma. I also have two things to add:
1. If you're going to throw some in later, remember to boil them first, or at LEAST freeze them. That sounds like it sort of defeats the purpose, but basil isn't nearly as free of nasties as hops.
2. I'd argue against using purple basil the first time around. I've grown probably a couple dozen varieties of basil, and purples tend to be very, very strong in flavor. Try a green sweet basil first, or maybe Ararat, anise (Persian), Mexican (for cinnamon flavor), or a lemon or lime basil.