The grenade will still have a timer when you drop it, so it'll take a little more skill than just simply pressing the right trigger.
Rapidly tapping the A button will help you crawl faster, but if you have a Grenade equipped when you're downed, you can press the right trigger (RT) to drop the grenade, and commit martyrdom. Now you can crawl around as a last desperate attempt for life.
In Gears 2 the poor chap that is downed isn't as helpless as he was before. The game will also include the ability for a player to duel with an AI or human opponent when both use the Chainsaw Bayonet attachment of the Lancer, as seen in the 2008 Game Developer's Conference promotional video, later confirmed in informal interviews with developers. He also revealed there will be a deeper story with new characters, new weapons, and new enemies. John DiMaggio, the voice actor of Marcus Fenix, confirmed to IGN that players would be able to fight Brumaks in Gears of War 2. The technical demo shown at the Game Developers Conference indicated that much of the core gameplay elements that were central to Gears of War (a third-person, 'run and gun' style game that emphasizes the use of cover) would be present in the sequel.