I have seen that is prohibited to daven while drunk (Drinking alcohol during davening).
How does chabad justify so much drinking on simchas torah while davening? I have seen shul sanctioned drinking to the extent where large numbers or shots of whiskey and vodka are consumed. Some people become visibly "drunk".
Additionally, even outside of chabad I have heard that we move birkat hakohanim to shacharit so that the kohanim are not inebriated. However, if one cannot daven drunk, there is still the problem of everyone else being inebriated during mussaf!