No, only openers that have a wall station (with push button, light switch & vacation switch) would be equipped to do that. It's possible, since you tried to reprogram the remotes and they didn't work, that the radio on the logic board is bad.
It's hard to tell but you could remove the logic board and look for burn or smoke marks on the logic board. If you see any then most likely part of the logic board was hit by lightning or a power surge. At that point you would have to either replace the logic board or add a new radio receiver to the operator.