how close do you mean to a fender?
i have an ibanez rg3270 which is mahogany back with maple top, and it has a middle single coil.
Also have a patrick eggle new york which is mahogany body, maple neck, ebony board and it has a wilkinson vintage strat-style trem and a neck single coil.
They sound pretty fendery to me (when those pickups are selected). I mean, any differences I put down as much if not more to the pickups (or the double-locking trem on the ibanez)- the blue velvet is a bit warmer and hotter than a vintage fender-style single coil, and the neck single coil in the PE is a hot ceramic single coil, so obviously neither is going to sound exactly like a vintage fender pickup regardless of what wood the body's made of.
Don't get me wrong, I'm not saying the body wood will make no difference... I'm just saying that if everything else is the same bar the body wood, it's still going to sound pretty fendery, just maybe a little warmer or something like that.
EDIT: after all that you'll probably try a mahogany-bodied fender-style guitar and think it sounds completely different, lol.