I positively know it will on the front, because I just had to change a set of shock/struts on my 2009 Silverado, because the left tire was cupping on the inside and causing a vibration....I actually thought I had a wheel bearing going bad, when I first noticed the noise....I may be comparing apples with oranges Jim....But, based on this experience and what happened with my 72 Nova years ago, it just waves a red flag for me.....I must admit though, I don't remember if the rear shock problem caused a tire wear problem on the Nova or not....However, I do remember it caused an annoying rear vibration issue.
Please see this about cupped tires:
http://blog.nwautos.com/2009/05/cupped_tires_are_real_--_and_a_real_danger.html
"There are two main causes of cupping. One is an inadequate suspension system. If your shocks are worn out and the tires are literally bouncing up and down as you drive down the road, every time they come down, they get scuffed, and that leads to cupping."