Yes you can, but perhaps you should not.
We really some kind of process to follow the finishing of the water, so I'll change your example to "continued up the mountain"
Now, whenever you feel like using past perfect, stop and think, could I actually use the past tense here. The past perfect is rare in English, and in most situation that you see learners using the past perfect you could correctly use the past.
We continued up the mountain after we'd finished all the water.
This is a correct sentence, but it would also be correct to use the past tense.
We continued up the mountain after we finished all the water.
It can be confusing to put later events before earlier ones so perhaps:
After we'd finished all the water, we continued up the mountain.
That preserves natural chronological order in the narrative.
This isn't really an "inverse past perfect". It is just a narrative description of events.