In-game? No, for a couple reasons. Your Pokemon are usually going to be a couple levels higher, and you're playing against a computer that uses stupid moves like Growl or Follow Me in single battles. And, there are barely any trainers who have a full team, so you'll have an advantage in numbers. You don't need the competitive advantage that EV/IV training gives you to win because there are already tons of other advantages.
Competitively? Yes. The competitive advantage given from investing EVs/IVs is usually needed and can make the difference between winning and losing. Investing EVs/IVs in Speed, for example, might allow you to outspeed tons of Pokemon that you couldn't before. Or, investing in Defense might allow to tank hits better so you can stall out a Pokemon that you otherwise wouldn't be able to defeat.
Chansey illustrates the effect of EVs/IVs perfectly. Before EV training, Chansey has a pathetic base Defense of 69 (with Eviolite, at Lv 100). After fully investing in Defense, however, her base Defense is now 178 (with Eviolite, at Lv 100). Combined with her astronomical HP stat, Chansey can now take Physical hits with ease. Before investing, however, she would have been very physically frail.