If you mean states saves, no. For in-game saves, the answer is yes, as long as "the other emulator" uses the common plain save format. Note that the save file name is case sensitive. For example, if your game file is AbCd.gba, then your in-game save must be named AbCd.sav exactly.
That happens to me but I can save it on My Boy Free by saving the game as quick save then when I quick load it, it says that I have to buy premium to load with out an ad if u wait like a couple seconds an ad comes up you cancel it you're back were you liftoff.