I found out about this from a SDA thread: -> https://forum.speeddemosarchive.com/post/gta_4_rerun.html. This was discovered by ExplodingCabbage, as far as I know.

Important info to know which precedes this part of the game (this is what I follow):

1. Make sure you have at least one shell in the combat shotgun after killing Dardan. This can be achieved by triggering the cutscene (no attention shot).
2. Pick up additional ammo from the shotgun guy in the apartment during "Concrete Jungle". (DO NOT switch to the sawn-off, just run over the gun)
3. Before the turn, shoot Ivan as much as you can with either the pistol or SMG.
4. Take the turn you see him take in the video. (the turn next to the propane tanks will leave you with less time)
5. Shoot Ivan, not the car.
6. Watch the video:

great find

When you pick up this SMG, you have 60 bullets. As you can see in the video, you can kill him in under 60 shots.

...but in the end you'd be taking a big risk just to save a few seconds. Getting this SMG after finishing Jamaican Heat (behind the bar) takes about 8 seconds. It's true you'd save about 6 seconds if you already have this gun during "Do You Have Protection" (because of the animation at the gun shop) and another 5 during Ivan. You're left with a few seconds of time save and even then it might be even less as I haven't precisely timed how long it takes to get to the SMG and back to a vehicle after Jamaican Heat.