Speaking as some one who has judged a LOT of contests, while we try NOT to let production influence the decision on song, when you listen to a LOT of songs, they all start running together. So the ones with better production will stand out more. But there is a bit of a trait you notice over and over on them. On the unproduced, work tape or guitar/piano vocal songs, you find them NOT as well written songs. The people who have the craft down and are serious about what they do, usually will have the more produced songs to compliment what they do. So you find those songs actually better written.

I've judged a lot of contests and can't remember a guitar/vocal song ever impressing me enough to pass it forward. They are usually not well written and not well represented,
Personally, if I was entering contests, and I have been in a few and won a few, I would never enter something that wasn't fully produced and well represented. Even if the prize was a professional demo. If I did that and won ,I would use the demo prize for another song.
But since most contests disqualify you if you have ever had a major cut or publishing deal, it probably doesn't matter either way. Just my opinion.

MAB