Generally, no. Each Guitar Hero (and Rock Band) generation/console used proprietary controller protocols and dongles.
Rock Band guitars/drums work on Guitar Hero World Tour and later (GH5, WoR, Band Hero) due to Harmonix/Activision agreement. Earlier GH games (GH3 and before) do not support Rock Band instruments.
Summary: Check the specific game's controller compatibility list. Dongles are usually game-family specific.