The purpose of draining it with cold water is so that it does not continue cooking , in fact, if you touch the pasta, it's not really cold, it's still warm. You're just going to suspend the cooking process, and since you're gonna put the warm sauce anyway, it's not really cold.
I do the same thing Clara ,when I feel its going to overcook ....and then add it to the sauce ,sauce being still cooking on stove-top...