Have your bike ready when you get into Mexico. If you don't speak spanish, you don't want to go tire shopping in a foreign language. Also, the rule for Mexico is Food, Hotels & Booze are cheap, bikes and parts aren't. If you do have to fix a bike, the cheaper labor will offset parts cost, but it may be a wash with what you pay here. Tire selection isn't great in Mexico, either. And you may find you have a uncommon / 'big' bike compared to 90% of the Mexican market.
Why waste a day fixing a bike, or worrying, if you don't have to.