Wrong. If they couldn't use religion to gain power they would have tried some other way to gain power, but nowhere is it said that they would succeed to the same extent. This is precisely the point: religion supplies a wide range of superstition that unprincipled people can abuse. If the superstition wasn't there, it couldn't be abused. Agree?
Let's do a thought experiment. Suppose Fred is an unscrupulous tyrant wannabe and wants to take power. His specialty is abusing superstition in the population. Unfortunately, in his country religious belief has been [noone knows how] removed entirely. So now he has to base his propaganda on other types of superstition. People who believe in ghosts, UFOs, psychics etc etc. Unfortunately for Fred, the percentage of such believe is far, far lesser than the number of people who once believed in god. So the number of people who are likely to be fooled this way is not 50% but maybe 10%. Ergo, the threshold to a power grab is higher (which is good thing?)
When you say "they would have used some other means" you are presenting the motive as the conclusion. You are saying that no matter what anyone might have done, they would succeed one way or another. This is not only cynical and fatalistic, it's also not particularly reasonable. It should be logical that the struggle for power is a competition between various parties and the party with the best advantage is most likely to win. Thus it matters a great deal what that advantage may be.