No, but you're not going to do very good without it. Wrestling and judo are fine, but where are you going to learn the submissions from? As noted, that's not judo's strong point and there aren't any submissions in wrestling. So you'll be able to take your opponent down with judo or wrestling, then dominate him on the ground with wrestling. But how will you submit him.
Beyond that, how are you going to counter the moves of someone who knows BJJ? And most folks--even people who are highly skilled in wrestling--feel uncomfortable on their backs. With a strong grounding in BJJ, it's likely you will, too.