Basically, the answer to your question is yes.
However, you will not be able to get a clean Item Valuation report as of monthend (which is used to tie to the GL Inventory balance) unless you print it at the exact moment that you have finished that month's billing (and receiving) but haven't started the next month's billing (and receiving).
Also, if you use the Order Entry tax reports, you will want to print those out at the same exact moment as above.
As for AR, your ideas are all correct. There is no reason to stop billing at month-end just because AR period end processing is not done, and you can back date the period end date.
Steve Schwartz