It will if I get it's temperature up enough before it enters the carburetor (or fuel injectors). It all boils down (no pun intended) to how much energy you put INTO the fuel to overcome that "latent heat of vaporization" problem. Heck, you could actually inject ALL the fuel as vapor with enough fuel preheat--although depending on how the preheat was done (electrical or exhaust gas heat), you might have to do the "startup/warmup" portion of the drive on an alternate fuel--and you'd have to be careful not to "overheat" the fuel to the point that carbonization became a problem.
This sounds a bit more like Smokey Yunick's "Hot Air Engine", which was turbocharged. Exhaust heat is the only reasonable method of accomplishing this, and with that much heat, much of the legendary detonation resistance of methanol and thus most of its benefits will be lost. The most influential factor on preignition/detonation is the temperature of the intake air, not the fuel or compression ratio.
The corrosiveness of the methanol will only be accelerated at higher temperatures.