I would not soffit. I didn't, and also vented the roof along the ridge, then covered the ridge vents with a ridge cap. My thought was that air would draft in under the overhangs and vent out the ridge line. I'm sure it does this as planned, but that in the heat of summer this wasn't enough...my girls were still getting too hot. I added vents on each eave end that close up in the winter. I live in the heat and humidity of the south, though.
https://www.backyardchickens.com/t/792316/my-4x6-pallet-coop-build-completed-pic-heavy#post_11409168
Lots of pics in my build...just skip forward to the roof detail
https://www.backyardchickens.com/t/792316/my-4x6-pallet-coop-build-completed-pic-heavy#post_11409168
Lots of pics in my build...just skip forward to the roof detail