As said above, there will be no significant benefit to removing the snow.
However, if your coop is not designed and constructed to handle the snow load (weight) than structurally speaking there is an obvious benefit and potentially a necessity to its removal.
I have built many out buildings and so designed my coop with the same strength in mind. The roof was constructed the same as that of most houses. 16" o.c. rafters, 1/2" osb decking, 30# felt, 3 tab shingles, with drip edge, facia, and gutters for rain water collection.
We've had snows exceeding 16" followed by rain and ice with no problems nor would i expect any.
If you're confident in your construction, let 'er ride.