I was under the impression that algae would prefer to get its nitrogen from ammonia as some additional energy consuming processes are required to use nitrate. Nitrate is used when not enough nitrogen can be obtained from ammonia. That would, in theory anyway, mean that algae could form in an uncycled tank. I would guess that it probably doesn't due to phosphate limitation. I will agree that tanks with positive nitrate test readings are probably cycled, but ammonia could still be present.
In this case, where ammonia tests show positive ammonia, it seems inappropriate to rely on assumptions rather than trying to find out why the elevated ammonia levels and indications that the tank had probably cycled existed.