You don't need to EV train unless you're battling competitively against others who have also EV trained. And I've found that doing proper EV training is virtually impossible while you're playing through the story, since good EV spots for the stats you're interested in don't always come along early on in the adventure, and the Pokemon trainers carry are always a wild card.
Oh it's definitely not impossible, faarrrr from that. The Pokémon you need for the right EVs are always close to the beginning, and in BW it's Patrat/Lillipup for attack, Petilil for special attack, Sewaddle/Swadloon for defense, Woobat for speed, and those are all available fairly soon in the game. Frillish and Stunfisk are for special defense and HP respectively, but I can't remember if there are any Pokémon for that in the beginning, doing this from the top of my head haha cause I EV trained so much in BW.
It is a pain though, because you have to keep track of the EVs yourself.
That being said I EV trained for a few months and then I was kind of done with it so I went back to normal training lol.