Yes, mahogany will need grain filler if you're going for a smooth gloss finish. No, red oxide primer will not dry translucent, but it comes close to the color we associate with mahogany, so lots of people have used it. It'll only be in the pores, so it won't color the whole surface. If I'm not mistaken, SG Heritage Red is Gibson's cherry red translucent over unstained mahogany. Try Guitar Reranch for rattlecans and info on how to reproduce that finish. I'm fairly certain that stain, or even dye applied directly to the wood won't get you what you want - it'll be muddy and lack depth. I'd fill the wood, seal, sand smooth and then shoot some kind of tinted clearcoat over the top until I got the color I was after, then clearcoat, cure and polish.