I don't recall that anyone has posted here on actually doing it, but...
It will change the overall flavor profile of the pork. Being the au jus was from smoked drippings, it would add that smoked flavor, but keep in mind you'll be inter-mingling the heavier flavors of the beef brisket with the relatively light flavor of the loin, so it might be a bit funky to get used to the taste.
Oh, being you're injecting, be sure to run a hot enough smoke chamber (about 250* or so, depending on weight) to get through the danger zone OK...(40-140* in 4 hours or less).
Another thought about the higher smoke chamber: you won't have as long of time for smoke reaction with the meat at higher chamber temps. If you have a bone-in un-injected butt, you can run lower chamber temps (225*) and get a really decent smoke reaction and stronger smoke flavor, for an example.
It's kind of a coin toss on whether or not it would be beneficial to the overall finished product, IMO, but it would be an interesting experiment, for sure.