I wouldn't recommend it, though I've heard of weirder things being given intravenously... Stuff isn't sterile, to begin with, and it's not isotonic, which means that the red cells might be damaged severely at the site of infusion (although at high enough blood flow rates, it sometimes doesn't matter as much: that'd be with a central line...)
IV fluids are NOT always saline, by the way.... D5W is used, for instance, and that's just water with d-glucose in it.
Weirdest thing I've ever heard IV: the fluid from the inside of a coconut. Early in the coconut's development, it's just a sterile electrolyte solution, and believe it or not, it was successfully used as an IV fluid... with the individuals receiving it surviving.
If you sterilized the Gatorade, and diluted it to isotonic concentration, you might get away with it, BUT there are flavoring agents and preservatives and all that jazz that might have toxic or allergic effects. As someone else commented, it's not intended for IV use, and the preservatives, flavorings and all that don't have to be safe for IV use, and probably aren't.
MD that's been around too long...