Ok, 2 other people already replied but i kinda just want to say this.
Think of EV training like this, you are scheduled to have a fight with someone who has know karate or kung fu or any other way of fighting, but you have time to prepare and learn a fighting style yourself.
Taking the the time to learn it would help increase your chances of winning, but even without it you might still be able to get the jump with the right strategy, but if you do both the training and the strategy your chances of winning go up by a lot.
Since this is pokemon, just replace learning a fighting style with EV training, it helps and can help like a hole lot, but it's not needed, especially if you are just on normal mode.
If you were playing on intense mode i would definitively say to EV train if you can, on normal you could probably get away with not.
If you decide do to EV train and have extra AP to use, you can get cards from the AP shop to unlock EV training rooms in the lab at Gearen which help make EV training REAL fast.
Hope this made sense and i hope you enjoy the game.