Can I change a recipe sequencing (parallelising consecutive steps)?

The idea is that the oil where you fry the chili, garlic, and basil grabs their flavor and aroma. And then the tomatoes are fried in that flavorful oil, which ends up in a much deeper and tastier flavor overall, as the tomatoes combine with the flavors present in the oil.

If you do it separately the tomatoes won't grab as much flavor from the chili, garlic and basil and you'll get a blander result.

The other question one could ask is about why can't we leave the chili, garlic, and basil in the pan. And the reason for that is that they can burn if you fry them for too long.

I think the flavor difference in this quick condiment will be minimal, and you should do a side-by-side to see if it matters to you. The real downside is you have two pans to clean. So your issue is weighing the gain of speed up front, with time lost of cleaning two pans when you are finished.

The downside is needing to wash two pans. That's it. If you're sparing with the amount of oil you use with the tomatoes, there should be no harm to the flavor.

That said, the best way to speed up this recipe is simply to skip the "remove the garlic and basil from the oil" step entirely. That's an unnecessary step. You might want to cook the garlic/basil for 30 seconds less, then dump in the tomatoes. That might not save you that much time -- maybe 1 minute -- but it will certainly save you effort.