Yes, though if you still feel you deserve the achievement in spite of it, you can edit the achievement file and give it to yourself.

This post made me realize that I may have been making a false assumption all these years. I don't remember the wording of the achievement. Is it to win with ONLY Capital Ships, or just not use frigates? In other words, can you use cruisers but not frigates?

Considering the game will award you the achievement regardless of the map or difficulty level of the opponent, most of these are pretty easy to get.  Try playing an easy AI on point blank and use the Sova Carrier against it.  Should be a piece of cake with the resource handicap easy takes.  Beating an unfair difficulty AI in a straight 1v1 is harder than almost all the achievements.