If you had multiple instruments sending to the same REVERB group, batch exporting the groups would not separate piano reverb element from say vocal reverb element, no.
I think to be able to batch export and keep the FX send elements separated you would have to have separate routing paths for them, even if the FX done on them are exactly the same. If it were practical to do so you could have multiple FX groups that all did the same thing but only received from specific instruments and outputted to separate groups. You could even link the duplicate channels so that whatever you did to one, the same was done to the others. But this is a burden on resources, tricky to manage, and the sum of the outputs is not necessarily exactly the same as if all instruments shared the same effect channel - especially dynamics control like compression.