Clerk may or may not accept that, or the judge might shoot that down. Depends who you're assigned to. Why? Fraud reasons mostly. If she shows and files her appearance HERSELF, and pays her appearance fee, then not an issue. Otherwise safe method is for her to be served.
Again, depends who you get assigned to. If they're "by the book" you will be sucking sewer water.
To to answer your question: If done right, weeks. If not, months, or longer.
I've had cases where this took as little as 2 weeks from start to finish.
Make sure all fees have been paid, that spouse has filed an appearance, that a "Certification and Agreement by Counsel" [which includes a STIPULATION AND REQUEST TO HEAR UNCONTESTED CAUSE] has been executed.
Also, ensure completetion of the "Affidavit & Waiver of the 2 year waiting period."
The author provides the preceding information as a service to the public. Author's response, as stated above, should not be considered legal advice. An initial attorney-client conference, based upon review of all relevant facts/documents, will be necessary to provide legal advice upon which the client should then rely.
I have not had problems filing my pro se opponent's Appearance. It's always better to have personal service, especially if something goes awry and the court must look back to "date of service," but that only happened to me once. You can get a court date fairly quickly but watch out for any local rule that prevents proveup too soon. I do not believe there is such a a rule in Cook County, but Will requires the passage of at least 30 days AFTER SERVICE. Also - make sure your prepare and serve a Notice of Motion informing your wife of the date you intend to go into court for proveup. There are also forms to fill out in Cook before you can prove up the case, and some judges prefer to have the Respondent present, especially when the case has moved quickly and the Respondent is pro se.
Bottom line - It would not hurt to spend an hour or so and pay an attorney to consult with you to make sure all your Is are dotted and your Ts crossed.
Best wishes to both of you.
As a side note, I would strongly recommend that your wife show up to any eventual "prove-up" that finalizes your divorce, even if she's already signed and agreed to everything ahead of time. You don't want there to be any question after the fact as to whether you wife really understood what she was signing, or if those were really her signatures on all the documents. That's really the purpose of why we do "prove-ups" that ask the parties in open court, on the record, and in front of the judge, if each of them understand and agree to everything being presented to the court as the final proposed Judgment.
A weekly guide with tips and legal advice for each stage of the process.