YES. The ability to communicate effectively is the basis of both advertising and public relations. Nowhere is this more apparent than in your writing, because the written word is most often your first contact with a potential client or editor.
As an English minor, you will do a lot of writing and that will definitely strengthen your writing abilities (i.e. grammar and spelling). If your main interest is public relations, though, I recommend taking as many journalism classes as you can or even trying to write for your school newspaper. The style of writing you use in a newspaper is very different from the style you would use in an expository paper, and public relations writing (press releases, public service announcements, etc.) is more closely related to the former.
Please feel free to PM me if you have any more questions
