No, mahogany is around 75% warm, or 25% bright. It's the exact opposite of walnut.
You can't really go wrong with something simple like Alder, or Walnut if you prefer. And then if you use something besides maple for the neck you should wind up in the right territory.
Don't fret too much over the woods. Bring it into the right neighborhood and the pickups/scale length/strings/hardware/electronics will do the rest.
Use pickups you think will balance well with whatever wood you choose, then adjust the electronics(pot values, cap values, treble bleeds, pickup selections, etc), strings(pure nickel wound if it's too bright, steel if it's too dark, iron/nickel if it doesn't have enough attack, nickel-plated steel if it's balanced), and hardware(aluminum/steel for more attack/treble/sustain, brass for a more balanced sound) until you get the sound right. Then there's also the amp and speakers you use.
There are so many other variables that wood winds up being almost insignificant except for looks.