I suppose various sequences would still work .... but in my opinion,
Overflow to wet/dry with mechanical filter media.
Small solids trapped on filter media, biological filtration for ammonia/nitrite.
Then the protein skimmer.
Finally the UV
Aside from particles getting trapped by the mechanical filtration - I don't think it matters all that much.
As the water passes by each of these devices, some of the waste is either converted or reduced - but not all is totally eliminated by the one single pass.
It's the continuous flow past/through this equipment that filters the water. Pass after pass after pass.
Since some is removed by each pass - it would make sense to me to first trap particulates to try and keep rest of the system clean.
Then pass the water over biological filter - knock down the ammonai compounds somewhat.
Then pass the water through the skimmer.
Finally run it through UV.
I'm sure if you hooked it up in various sequences - that the system would still function.
A snapshot of time would be gallons per second. How much wastes, ammonia, nitrite, dissolved organics and parasites are reduced each second ???
The filtration can also be looked at in total flow for gallons per hour/day/week.
It's this continuous flow past filter media/equipmenet that really makes the big difference.
Each time the water passes past a stage - the equipment in that stage does perform "part" of it's job.
It the continuous flow past each stage that gives you the accumulated effect.