I use saved searches with Stylesheets all the time.
Somewhere, waaay back

someone decided to NOT (allowing) store the scope of a search.
Stylesheet searches MUST be done while
viewing the sheet AND the scope is
CURRENT FILE. Other than that, saved searches run just fine. That includes running a Group of searches ON THE stylesheet.
FWIW

I created A
Group Just for Stylesheets searches ( I have lots of other groups. Including Groups within Groups that do a series of other S&R tasks)