No, there would have to be a good reason for me to avoid a battle. Case in point I'm in the middle of ev training in the area and fighting this trainer would yield evs for the wrong stat. Or perhaps there's a glitch you can perform involving said trainer so you want to keep him available for later on.
In normal game play though you want to gain experience through trainer battles so that your Pokemon can level up. You also have to keep income flowing in, tms, pokeballs, daycare services, vitamins, breeding and healing items all cost money :)