In the future please post scans of the card(s) in question. This helps assure an accurate ruling. However this is actually a general ruling that doesn't apply only to Fighting Fury Belt, so I'll go ahead and answer it.
An attack needs to do "some" damage before it can do "more" damage, or any other damage modifiers can be applied. An attack that does no damage at all will still do no damage even if the Pokemon using that attack has a Fighting Fury Belt, Muscle Band, or any other damage modifier in effect. Note that the effect of "placing damage counters" is not the same as actually doing damage.
Additionally Raticate is an Evolution Pokemon. Fighting Fury Belt has no effect unless it is attached to a Basic Pokemon, so in the case you outlined it would do nothing.
