After receiving a NOID, one would submit a response to the NOID, not an appeal/motion. If there is a denial, the appeal/motion can be considered. Speak to an attorney as a number of questions would need to be asked of you in order to provide a good answer.
Kindly note that this posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Remember, this site is akin to an internet blog. Do not rely on information here to make important decisions in your life. Make an appointment to meet with a licensed attorney in his or her office (or via Skype or phone) to obtain competent personal and professional guidance.
You cannot appeal a NOID, you can appeal a denial. Your spouse's status after filing an appeal depends on what you are appealing and what was her status before. There is no set amount of time it takes CIS to process an appeal or motion to reopen, and in addition, it may depend on what you are appealing.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
What are you going to appeal? There is no decision yet. You or your lawyer should respond to the NOID and persuade USCIS there is no reason to deny.
This answer is for informational purposes only and should not be construed as legal advice.
Best to discuss it with your lawyer. If you don't have one, Avvo has a terrific "find a lawyer" tool so you can find a top-rated (10) Avvo lawyer within a mile or two of your house.