When you're pitching your songwriting demos there is always a debate whether you should do a simple piano or guitar vocal or a full production. I don't think there is a correct answer. A great song should shine through regardless of the production. However it can depend on what genre of music you are writing in.
If you're writing in country and its a pitch to a publisher it will probably work. If you're writing in pop or hip hop you're wiser to do a full production. Some people are not as good at imagining what a full production of your song will sound like. So if its a pitch to an artist or a record company a full songwriting demo might be better.
If you have a low budget you are wise to make sure the vocal and what production you have is as high of quality you can get or afford.