It really is the way to go. I also do this for chickens. Provided they fit in the pan, I just set them in the pan and smoke them.
I just pour all those drippings into a tall glass and skim the fat from the top and use the fat to replace some or all of the butter when making the roux. I use the liquid from the drippings as the liquid to make the gravy, usually adding a little cream and milk to give it body.
Best damn gravy ever in my opinion. Flavor matches the meat.