Very few things in life work better when you're completely plastered. Obviously, there are exceptions, and there's a very good reason why the military used to dish out rum tots before engaging in combat - being slightly squiffy can even make going over the top and running at a machine gun seem like a good idea. Construction workers on the Channel Tunnel, enjoyed very liquid lunches by all accounts, there's a corresponding death toll on that project which bears testament to the fact that heavy machinery and an all dayer, really don't mix. So, unless you're a pirate, being paralytic doesn’t work. Not even for hard drinking rock stars, as anyone who's seen Shane McGowan tried to sing whilst full to the brim with booze will testify to.
So, that brings me to the question of drinking and a best man speech. I don't believe in total abstention. If you don't have a drink until you're done, you're going to see the end of the speech as some sport of party finish line, and will race towards it with single minded abandon. All you'll be thinking about is having that beer or wine, and your performance will be corrupted, notwithstanding the fact that a couple of beers will almost certainly calm you down.
The danger is having not enough willpower to stop at 2 pints, and you suddenly find yourself on the wrong end of an accidental booze bender. In the whole history of best man speeches, nobody ever landed one whilst being unable to string a sentence together. So, have a couple of relaxed drinks, keep it at that, and then drink whatever you want when the standing ovation has finally subsided. Your audience will thank you for it, and you won't suffer the PTSD that comes with being yet another drunk best man.