Yes, as long as you submitted the paperwork before the expiration date, you are fine. Just be sure to carry the documentation that proves that it is being processed so that if you are detained for document inspection, you wont have any trouble.

To reply to your question I will need to know the type of visa you have.  For example, an "L" tourist visa has three governing factors, validity, # of entries and stay.  On such a visa, you can enter China on the day itt expires if you have an extra entry, and stay for the number of days allowed even if your visa has expired.  But with a work "Z", or a student "X" visa, the day after it expired you are in China on a non legal status, and subject to fines and deportation among others.  So, I would not request a new visa on the day it expires to avoid any misunderstanding from officials who interpret the law in a very rigid way.  Try two weeks at least before it expires so you will have no headaches.  While you are requesting a new visa, will you stil be in China without your passport?