Does "Boost" module work together with "Theme Key" module?
The two work well together (Does ThemeKey supports Boost caching) with the caveat:


  ThemeKey supports page caching and external caches like boost - if the
  page is cachable.
  
  If you switch a theme depending on the user's browser, the page isn't
  globally cachable at all, because other users are using different
  browsers! That's not a ThemeKey issue.