It would not initially. However, if there are a few big successes, the cost of living would rise. But even then, it would be concentrated in the areas considered attractive to the newly successful company employees and people in the secondary economy serving them.
Unlike NYC and SFO, we are not a port city. We have functionally "infinite spaces for suburbs, and no geographic boundaries". We aren't on the water, and 2-3 directions on the compass you hit forest/fields really fast.