Food for thought: Many genes can code for multiple protein products through a process called alternative splicing. Some of these alternative splicing products are abbreviated versions of a longer protein coded for by the same gene. Considering this, would you still hold to the statement above?
I would have to study alternative splicings more thoroughly before I could give a good answer to your question. However, my initial impression would be that an alternative splicing is just a copy of the original which left out part of the protein coding. I don’t believe that this contradicts what I was saying since (If I correctly understand what you are talking about) no new information has been developed instead a part of an existing protein string has been copied incompletely. This still does not show that natural selection would favor a mutation which produces a new sequence of bases which partially codes for a new protein. Since the partially coded protein cannot yet convey any benefit on the organism.