Zands, I took a beekeeping class at fairchild farm a few weeks back. They stressed several times that one chooses hive location carefully because once selected, the bees will continue to return to the exact same spot. Noris was saying that they had to move the hive location for different reasons (including putting the hives in the netted mango breeding areas...(for the sake of this argument, let's pretend they were apple breeding enclosures, b/c i am no expert). When they move the hives, she said richard has to take them home to his house (3 miles away) so that when they bring them back, the bees "forget" the old spot and come back to the hive.
I do not wish to argue whether or not bees pollinate mangoes, and don't claim that this information is perfect, but it was what they passed along to us, from Noris and Richard's experience--bees will not be happy if their hive location is moved, unless taking them more than 3 miles away for a day or two.
I do agree with Rob that Walter knows more on the subject than I, or anyone else here in FL. If you have other trees, however, it seems like a moot point...put the garbage can out there for mangoes (or don't if they set plenty of fruit), raise the bees for honey, and get better pollination on other fruit trees, and veggies in your yard.