I always put BBQ sauce on my chicken after it is done baking, but I was wondering if I can do the same while seasoning it to save time?
Yes, "It is possible"...however there are trade offs. The sauce will caramelize and become a tasty glaze...but...your chicken becomes more 'braised'(cooked in liquid) than 'grilled'. You get the caramelized sauce but loose the 'maillard effect' that comes from grilling. As taste is personal matter the best advise is try it and see which you and your audience prefer.
On an aside, you might try doing a brine (long soak) or marinade (other than the viscous BBQ sauce, for instance soy sauce) and/or even injections to layer different flavors.