No, you wouldn't be able to use your tremolo if you're stringing through the body.
You'd probably get the best results ditching the tailpiece, and drilling the stringholes just behind the bridge- the sharp angle at which the strings would go over the bridge would improve string tension and sustain, it'd pratically be a Telecaster.
Either that or drilling behind the bridge plate for more Venus stylee setup. You wouldn't be able to drill on too much of the plate because of the tremolo route in the body underneath.
