No. Alignment sets the geometry of the wheels, they don't do anything which will measure forces generated by the tires. Usually if a car pulls it is because the problem tire is on the front. You can temporarily swap the front left and right tires and then drive it. If the tires are the problem the direction of pull will reverse with the swap. Do not leave it that way, but it is safe to drive for a mile or so with directional tires "backwards". Alternatively, swap the tires on the left side, drive it, then the ones on the right.
I have had this happen to me several times. A tire develops a pull and it has to stay on the back and can't be rotated forward because the car drifts too much when it is on the front. If the tires are new and you find one that pulls like this take it back and get a replacement. Tires can develop this problem from hitting potholes, uneven wear, or who knows, maybe gypsy curses. It is pretty common.