not exactly; many of those regions that we knew were junk weren't genes, but long regions of repitition of archaic junk that was inserted by viruses and replicated unnecessarily tens of thousands to millions of years ago. Generally, most scientists don't think that (for example) alu sequences really have strong function that you could measure in an experiment.

For example junk DNA was described before we really understood that RNA genes were common and so large regions of the genome that are RNA genes were just treated as totally non-functional.

Sean Eddy proposed an interesting experiment called the Random Genome to address these questions but I don't think anybody is seriously considering running the experiment.