Will it be faster to render smoke and fire separately and then composit together or not faster?
I don’t know about speed, but very-frankly I think about control. Specifically, "keeping my options wide-open when I start to composite(!) things together.
“‘Smoke’ is one thing, and ‘Fire’ is another.’”
Furthermore … “what’s the cheapest-and-easiest way to get ‘more smoke,’ or ‘more fire?’” Uh huh, you guessed it: “composite the stuff on top of itself, offset plus-or-minus a few frames.” Cheap, effective, easy … no 3D-rendering required.
Whenever possible, I would advocate that you should focus on one visual effect at a time. Particularly when one (smoke) has to do with the occlusion of light, while the other (fire) has to do with producing it.
Frankly, I would not deal with these two objectives “together,” unless I could convince myself that I had to.