If your cells can tolerate it, you'd probably see a larger activation (relative to the untreated) with a serum starvation in low serum media. In the presence of serum, you could possibly have some level of activation of your desired protein due to the presence of a myriad of growth factors. That said, some proteins are activated so robustly by growth factor treatment that it doesn't matter which treatment protocol you use.
Above answers can be followed, for my experiments I always like to starve cells overnight in presence of 0.2%FBS............always works for my experiments..............especially for Growth factors...................good luck