No, all men won't switch off.
And, forgive me for asking a silly question, but why do you think we'd mind if they did?
I accept there are huge and important positives to having men who are committed to equality, to feminism.
But, along with them, come all the other men who are not simply 'switched off,' but who are passionate about feminism and want to destroy it. F4J, for example.
I have to admit, and I hope this isn't offensive to 'switched on' men, that I suspect for many feminists, the total effect of all men 'switching off' feminism would not be quite as devastating as you seem to imagine.