no.
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There aren't any quick balls in emerald as far as I know :(
you cant get a heavy ball in emerald
you cant get a timer ball in emerald
No, you cannot get a Quick Ball in the game. The Quick Ball wasn't introduced until Diamond/Pearl/Platinum, which was released after FireRed.
You cannot make a quick ball using apricorns, however you can make a fast ball from the white apricorn.