Just a quick question; Do people take sitcoms to the fringe to showcase them?

yes

I believe contrary to what you might expect the best way to get your sitcom on radio or TV is not to submit it to Edinburgh, but to do a different show.

The reason being the best show in Edinburgh wins the Eddies (formerly the if.com awards, formerly the Perriers). Eddies winners can go on to radio or TV shows.

But as far as know, winning shows are not stage versions of sitcoms.