Your starter will absolutely take on the local flavors. It is this process that made San Francisco Sourdough what it is/was. The foggy salty marsh air carries a bacteria named for the area Lactobacillus sanfranciscensis. This is what gives the tangy flavor not the yeast.
I was an all grain home brewer for 25 years. At one point in time I had over 25 live yeast cultures that I kept alive for brewing different styles of beer. You could chain brew 3 or 4 batches off the same yeast by just washing and pouring from fermentation to fermentation but sooner or later the local wild yeast and bacteria would get a foot hold and ruin the true flavors. This was not always bad but not true to style. It is the same with bread yeast starters.
Over the past few years I have collected a couple of large dutch ovens and so I am thinking of giving them a go.
