You can do that but for steaks (especially) that I am going to grill I don't bother. If I really want the pan juices to be a major part of the reduction then I simply cook start-to-finish on and in the oven, or use an alternative as noted below.
You can get a lot to go on by using other methods for grilled steaks. You can start your meat on the grill indirect and then finish with a sear. Move to a piece of foil for resting and loosely cover with some of the foil. Add any juices that collect to your pan sauce. (If you make the pan sauce a little thicker then the added juices will thin it slightly and add good flavor. That's what I did
here. I sautéed a little shallot in a little butter then added a small handful of currants and a fair amount of cranberry juice. This I allowed to reduce while the currants were rehydrating. Then I puréed till somewhat smooth, finishing with cognac vinegar, salt and pepper. After the rib-eyes rested I added the collected juices to the sauce.)
An alternative is to season any trimmings you have (fat, lean, both) in the same fashion as you season the steaks then use the trimmings as a sauce base, searing them well in a pan and building the sauce from there, just before or while the steaks are on the grill.
Two other methods (either of which I use if I am wanting to grill but want a pan sauce substantially based on beef juice reduction) is to buy a sutiable small cheap piece of beef at the same time the steaks are purchased and treat it like the trimmings I just mentioned above, or use homemade beef stock and flavor it according to the seasoning you are using for the steaks and/or in a complementary fashion. In both cases it is still worth adding rested meat juices from the foil to the sauce.
Quick note on that: If you serve the steak(s) sliced, as I often do, you can slice either while they are still on foil or you can move them to a small cutting board on which you can collect juices during slicing and add these, as well, to the sauce.
