Sure, the main story is crucial for game progress in GTA 4. Think of it this way: the main story is like the spine of the game. As you complete main story missions, you're not only following the plot but also unlocking things like new vehicles that you can use to explore more of the game world. Plus, your reputation within the game world might change as you progress through the main story, which is all part of the overall game progress.
Yes, the game progress in GTA 4 is closely related to the main story. When you complete main story missions, you unlock new areas, items, and sometimes new gameplay mechanics. So, the main story is a big part of how the game measures your progress.