You can't touch anything in the standard diving/snorkeling places, which are all reserves. However, there are a lot of other areas that are outside the reserves. If you go with the usual dive tours, the guides won't let you touch anything even if you aren't in a protected area. I assume you will be on Ambergris Caye? There are signs at some of the shops in San Pedro that advertise collecting trips, so if you want to bring something back, you'll probably want to arrange to spend a day with one of those guys. They can take you to the areas where collecting is permitted, and tell you what may be collected.
Cheers,
Don