By this I mean, say you have your 3 killstreaks, and first highest killstreak is Chopper Gunner (imagine your other two are EMP and Tac Nuke). Ok, so you have you 11 kills in a row, and you have chopper gunner available. You begin running around shooting your gun into the air to attract enemy attention. You are shot and killed.
Now, you respawn, with your chopper gunner available. You find a nice quiet place to hide to activate your chopper gunner.
Now, imagine you are really good at chopper gunner and quickly rack up 13 kills with chopper gunner. You manage to get through the whole killstreak without having your Chopper Gunner shot down AND you do not die while using chopper gunner. Remember, you killed 13 people with chopper gunner.
THE QUESTION: WILL I HAVE EARNED ANOTHER CHOPPER GUNNER AS A RESULT OF MY FIRST CHOPPER GUNNER?
Best Answer
Kills you get using killstreak rewards gained on a previous life after you respawn do not count towards new killstreaks.
So to answer your main question: no.
Also see here: Which Modern Warfare 2 Killstreak Rewards count towards your current kill streak?