yes, that's what an index is all about
also, there is an improvement on the current FTI search coming for 7.3 where the timeframe is 'self JOINED' in to allow the mysql engine to include it in the optimization. FTI by definition/design only uses the one index and says 'screw you' to any other columns the might have indices.
This pulls the time field in with the JOIN on itself.
so your queries will just get faster
