What impact does the order of assembly have when making cookies?
Generally with baking you mix all the wet ingredients, then all the dry, then incorporate the latter into the former. This prevents clumping and helps make sure everything is mixed uniformly.

In some recipes, adding the eggs (often un par un, or one by one) also contributes (via the yolk's supply of lecithin) to emulsifying e.g. butter and milk together. 

The best way to find out, of course, is to experiment. Next time you're making these cookies, make a double batch. Do one according to the recipe, and the other your way. Honestly with cookies I doubt you'll see much difference; they're basically foolproof (I have, when in a hurry, made chocolate chip cookies by dumping everything in the mixer, whacking it about with the paddle attachment, and then folding in the actual chips. Worked fine, basically). When it comes to baking things that are more finicky--cakes etc--I would follow the recipe directions.