If they could manage to pin it down somehow, I think they might, but they won't actively hunt fish down. Normally they'll sift through sand to find crustaceans and such to eat. Their mouth is under their bodies, behind the eyes, so it's almost impossible for them to catch a moving fish with their mouths. Of course, perhaps at night if a small fish rests on the gravel, it'd get sucked up. Also, sturgeon don't have teeth, so I'd be worried about a small fish being a choking hazard.
I believe gars are temperate water, not cold water, so they'd probably like the seventies better, with temperature rises during the summer to give them a growth spurt. Sorry, but I don't know much about gars, they're illegal here. I don't think I'd trust an alligator gar with anything but fill grown arapaima, though. Their jaws look formidable.