I want to allow the final coat a good couple of weeks to cure before moving in with several large area rugs. I want to work elsewhere in the house and for the area to be finished when the floor is done curing so I'm considering painting the walls now. I'm thinking I should clean thoroughly, cover in paper and plastic and paint. I'd be done in about a week and then I'd pull up the paper, screen, clean and begin the finish.

Out side of the obvious (spilling paint, dropping something heavy and denting etc) is there any inherent issue with sanding, waiting a couple of weeks then applying stain and poly? I don't suppose but I'd figure to ask.

Its fairly common to sand stain and coat floors, then hold the final coat (mainly in new homes) Works okay as long as you are careful.
If you do cover it, be sure toi give it some time to cure (a day or 2) before covering it.
Dont put tape directly on the floor. blue tape green tape purple tape. NONE Its better to not rick it and just tape to the baseboards, and other peices of paper.
And also if you do cover, cover none or 100% of the floor. This will help discoloration from the sun ect.