Yes, I mean of course it will still drain, but that's more due to battle than the form itself. I'd think Base would do the same thing. Goku was banking on that KHH finishing Cell, he applied way more power than he would for a normal attack. It would have drained him no matter the form.
Either way, I think Goku not using SSJ against Hit is just bad writing. Yeah you can argue he may lose 1% of his stamina or whatnot, but he also raises his power 50x (or whatever the fuck it is these days). 50x power increase > losing 1% stamina.