A little cornstarch should, if you add it with the bbq sauce, make it just thick enough to cling together a little better.
I'd say make a slurry of say 1/2c water, 1/4c bbq sauce, 1tsp cornstarch and add it to your ground beef. Let it cook down (I'm basically thinking how taco packets work here) until it's close to where you want it; continued heat in the oven should finish binding.
Or skip the bbq sauce, use dry herbs and spices mostly with just a tiny dab to bind it together.
Also you just made me want a patty, you awful man.
As the others have mentioned, it won't quite be the same ... however, it can be done, it just won't quite have the same flavor as there isn't a chance for the meat juices to transfer into the sauce, and some issues regarding mixing it back in with the cold pasta.
If I were going to try it, I'd brown the meat, remove some of the fat if it's a really fatty grind, then add some extra sauce (or even other liquid ... maybe dairy, for a classic bolognese) to let it simmer for a bit ... then toss the pasta in with it to reheat.
The extra sauce is the key, otherwise, the meat isn't going to blend in with sauce on the pasta, If you reheat the pasta in the fresh sauce, it should hopefully mix together more completely.
... but if I were to do it, and wanted to add a meat to an already cooked pasta, I'd probably not choose ground beef as a first choice; I'd probably cook up some sausages, cut it down to an appropriate size for the pasta you're dealing with, and mix that in, possibly adding some extra liquid when reheating the pasta.
Best Answer
The Magic Bullet is essentially a blender, and is, as such, inherently unsuitable for making a salsa.
Also, the "seven-second" part of that recipe is a lie. You're still going to have to peel the onions and garlic, remove the stems and seeds of the peppers, and trim up the tomatoes.
You're getting your knife and cutting board out anyway, so why not just do it by hand? It really shouldn't take more that 5 minutes.