Does a 15,000 BTU Burner require a larger gas line?
I believe that the size of the piping does matter. In Heston Blumenthal's The Fat Duck Cookbook he tales an interesting tale from the early days of the restaurant. I found the story online (2nd paragraph):
http://www.guardian.co.uk/lifeandstyle/2001/nov/17/weekend.hestonblumenthal

Excerpt from the article:  


  Traditionally, we have always been told to plunge green vegetables
  into a large quantity of boiling, heavily salted water, so that the
  quantity of cold beans added was not enough to bring the water off the
  boil. The old Fat Duck kitchen was fuelled with gas from a domestic
  pipe. This meant that we could not, in fact, bring a particularly
  large quantity of water to the boil. Because of this, we had to cook
  our green beans in batches of about eight at a time. Any more than
  this, and the water would come off the boil, leaving the beans more or
  less to stew and develop a murky brown colour.