Not at all. The institute is very corporate in design while Big Mt is very wacky sci-fi.
Well, they're both high-tech enclaves (with a small "e") that make use of humanoid servants, I suppose. Thematically, they seem very different however.
What influences did you have in mind?
Unfortunately, Bethesda is incapable of that level of writing. They build awesome worlds, but fall short with the pen (or keyboard) IMO.