Your skin's tendency to scar (assuming its skin we're talking about here, but also applicable to internal scar tissue) depends on several factors: inflammation, healing time, moisture, genetic proneness, etc. It also has to do with the hyaluronic acid levels in your body, which decline with age. A diet high in hyaluronic acid (sweet potatoes and bone broth are good sources) and nutrients important for skin healing (zinc, magnesium, Vitamin A, etc.) may have some effect. In general, eating primal should help with healing wounds due to its being far less inflammatory than the SAD, and I doubt it would increase your chances of scarring.
Old scar tissue will typically stay the same unless you break it up with strong acids or a process like needling. Your body treats scar tissue the same way as normal skin, and will not suddenly wake up and realize that a scar is there and start cannibalizing it when you eat a healthier diet. HOWEVER, when the dense scar tissue is broken up or dissolved, healthy skin with new collagen has a chance to take its place, and eating a healthy diet should help with this process.
Topical agents like copper peptide and hyaluronic acid serums may be helpful in repressing the formation of scar tissue, and combining them with a good diet may make their benefits even more apparent.
I'm still scarring from acne since going primal a few months ago, and my older scars look the same, but maybe after a year there'll be a difference. Reversing scarring takes a LOT of patience.