I believe you can't shoot and sprint at the same time, but you can maintain locked aim while running.
Which brings up another weird, counterintuitive implementation: Because lock-on aiming keeps your reticle perfectly locked on a target, as players we've been taught to think that our bullets are actually landing there. But guns in GTA4 do much more damage if you're kneeling and stopped. A lock-aimed, manually adjusted headshot from kneeling position in GTA4 multiplayer is commonly a one-shot kill. Shots to the torso are similarly more effective when stationary, but if you're on the move, you can unload an entire clip on a aim-locked target and they won't fall down.
It would have been interesting for them to allow lock-on aiming only when stationary, and allow for only manual aiming when on the move. They probably tried that, and something about it didn't work. All I know is the mp games with aim-lock disabled play a lot differently than the ones with lock-on: cars are deathtraps in lock-on games, as the aim remains perfect.
For extra LOL-points, try using the GTA4 cover system during any multiplayer game. It will get you killed faster than running around in a leaning, Euphoria-enhanced circle.
But back on topic: that movie is interesting because it also has a sense of speed while on foot. I bet the first thing they did when the transferred to first-person is realize how ridiculously slow the turn-rate is for poor Nico.