Hardly. Genja routinely proves he knows what to do as adc for his team. He's never ridiculously far out of position during teamfights, he almost always is one of the last, if not the last, man standing after heavy teamfights, and routinely keeps up and exceeds enemy adc gold through better farming. You get all the focus on Gambit's mid, top and jungle because they initiate everything and dive balls deep on everything, but if you watch Genja through an entire match, if he's not grouped up for a fight, he's farming. He's not derping around, following his team waiting for a lucky find, he's farming because he knows when late game rolls around, that 20, 40, 50 cs difference he made will mean magic in terms of damage. And he rarely gets caught while doing it, even when pushed past enemy outer turrets. The only time he's not farming is late game when he's full built, or when it's time for a teamfight/global objective.
Edward, while a good support, is certainly not the reason why Gambit's bot lane was successful.