The non-coding genome is a large part of what causes us to look different from a mouse or a fruit-fly. Gene regulation (what gene to transcribe, and when) is largely controlled by non-coding DNA: https://en.wikipedia.org/wiki/Regulation_of_gene_expression
There are energy costs associated with useless information being stored and transcribed in the genome... so it is pretty reasonable to believe that information theory does play some (however minor) role in how data is stored.