Yes modern tanks FCS can do that, it's actually bad idea for helicopter pilots to hover in range of modern tanks armament, surprise APFSDS, HEAT or HE round is not nice. ;)
BTW for all players, as a RHS member doing research mostly about AFV's, and also as Steel Beasts Pro PE simmer, few advises.
Laser range finders cooldown, yes this is real feature (kinda ;)) because laser range finder in the past could burn out, the modern ones do not burn down but system turn them off for some time to prevent burn our if laser range finder is used too often.
Now for lasing, lead and overall gunnery.
When you have a moving target very effective technique is so called "laze and blaze", which means that you track the target for around 1-5 sec, then laze it, and after around 1-2 sec of steady track fire the main gun. What is always important is to have steady track on target. Also it's necessary to keep up turret rotation speed properly to target movement speed, it is possible that with too quick rotation, even if you have steady target track, FCS will overcalculate lead, which means miss.
I also strongly advise everyone interested in this subject to read Steel Beasts Wiki about gunnery, I will provide links for two most popular tanks in the sim at the moment, this is M1A1HA and Leopard 2A4 as they are kinda, basics for each gunnery training.
I hope this will be helpfull, and interesting for other players, cheers! ;)