Melee - Definitely. If you hit someone in the head, it should daze them, and if your weapon (and weapon skills) were powerful enough, they should be knocked to the ground. Same with hitting someone in the legs, sweeping underneath them or simply crippling them from pain.
Ranged - Again, depends on where you hit them. If you're shot in the chest with a powerful enough weapon, you should have a second or two before your body registers the pain. This gives you a second or two to shoot back (with serious penalties to your stats, you're still shot after all) before falling to the ground from pain. Being shot in the leg should, in most cases, immediately drop you to the ground. Crawling would still be an option, maybe to get behind cover, but with serious pain along with it.
It all depends on how much pain you're in. If a bullet doesn't pass your pain threshold, or didn't hit a joint or something vital, you shouldn't drop to the ground. I'm all for this idea, it's not just "shoot for the head to win", getting shot to the ground could be just as advantageous.