I would bet you get answers yes and no.
I personally do not leave barrels in.
I typically finish my steel before I finish the wood....or it's all being done at the same time. I don't want finish on my steel...or any of my other parts. For me, everything is off the gun...I haven't built anything with inlays or anything that really isn't meant to come off though..
Just obviously have to be careful with the forestock.
I don't have the time for slow to cure finishes or finishes that require sunlight. If it's really nice out, I might put them in the sun...but typically not till the finish is dry. Nothing worse than pollen, bugs, etc all stuck to a rifle stock.