I have the Ascent jacket and have worn it mostly for September elk hunts. It is a little heavier than the Core material, but it's also a very different material than the Core. I usually have it on first thing in the morning when it's cool, but once late morning hits and the temps start climbing, I put it in my pack and just wear my base layer shirt until late in the evening when it starts cooling down again.
I would think you would use it the same way. It's perfect to give you that little bit of extra in the morning and evening, but it packs away easily during the day when it's warmer.
For reference, my elk hunts are probably low 50s at daylight and I'm probably coming out of the jacket mid morning when it gets to the mid 60s.