Since I moved my ridge line to the outside of my bug net on my HH and slept on top of it I can say I'd personally rather be able to get in an out of the hammock faster than deal with the stupid HH door underneath all my insulation but that's a very individual response. Something to keep in mind if you get up to use the bush a lot during the night.
I can definitely say I noticed it feeling warmer when I crawl back into my hammock even before I get back under my blanket, but you've also got a lot of warm thermal mass in there with the blanket/sleeping bag.
Some testing may be in order but I'm inclined to think that the micro climate effect is minimal at least in terms of heat retention. I totally vouch for the ability of the mesh to block some wind which will make it feel warmer than without.