No, it is very unlikely to win a tournament with no EVs. EV training is quite simple. Basicly, when ever you beat a Pokemon, you get certain EVs which ever so slightly increase one of your stats, eg. Blissey gives you 3 EVs in HP. The most EVs you can put into one stat is 255 and altogether you can only have 510 EVs ( though 252 EVs will give you them same stats as 255 EVs except you have 3 left over). Power items like the power bracer increase the EV gain in a certain stat by 4. Pocket Virus (or Pokerus) doubles the amount of EVs you get in every stat ( power items take effect before Pokerus so it is +4 then x2). Pokerus wears off unless your Pokerus Pokemon is in the PC, so you should keep a Pokemon in the PC you don't need to keep the Pokerus. Pokerus spreads to other Pokemon in the party when the PP (Pokerus Pokemon) defeats other Pokemon and trainers. That's about it please choose me as best answer, hope I helped!
-Anonymous