Fury had a 39-55/tick mana drain from launch until the Jan 9th, 2001 patch, when the mana drain was replaced with a Dex buff.
So yes it should drain your mana pretty fast. But the good news is, around Velious release, it stops, or at least it should.
If Green is in or past January 2001 era and Fury is still draining mana, that may be an era spell bug for Telin to fix
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