This has been done with mice, with no observable effect. I think wikipedia's page on junk DNA references the study, which I haven't looked at myself.

edit: The paper is behind Nature's paywall; here's a copy. They didn't notice any effects at a macro level. When they checked gene expression levels, they found two differences; but at p<0.05 from over a hundred experiments, which seems suspect. They did another test which I don't understand but which seems to show some difference between the experimental groups.