I recently added "Great Stuff" foam to my Tikka T3 Lite, not to add weight, but to reduce noise from scraping against brush in the field and to insulate the stock to help make it warmer to the touch in cold weather. It worked fine.
I didn't want to add weight, so didn't think of adding lead shot, but if it were to be added, a concentration located parallel to the bore might help to keep recoil straight back.
If I can't be with the rifle I love, I love the rifle I'm with!!