Can a chemical peel reverse sun damage to skin such roughness and spots?

Yes. There are different peels available. I like the ones containing Retin-A and hydroquinone or abutase for removing sun spots.
Reverse sun damage. Chemical peels are a great way to reverse sun damage and correct textural and pigment irregularities to smooth out the tone and complexion of skin. A cosmetic surgeon or dermatologist are best options to discuss peel options and treatment schedules.
Yes. Chemical peels are one option for reversing sun damage. There are others as well, such as laser dermabrasion, microdermabrasion, and various fractional laser treatments. See a dermatologist who does these kinds of cosmetic procedures. Keep in mind that insurance seldom if ever pays for treatments like these.