It's not applicable if you go with the foreign diploma proof, but If your wife studied in English in university, there is no "studying" required here really. The IELTS scores needed for citizenship, 4 in speaking and 4.5 in listening if I remember correctly is pretty much a formality.we are planning to go to iraq anyway. And certifying it is less then 50$, also no studying required and no need to think about passing this and the actual citizenship test. We save money and also save time.
Also, for university graduates, the citizenship test will also be a formality for anyone who the book once or twice and does a few practice tests. A few hours of preparation are all it takes. It's easier than the easiest university exam. Most people I know got 19 or 20/20. So, unless your wife cannot get a few hours of study time at all (and tous said she "started studying", so she's already very close to be done studying!), don't even consider that as a reason to postpone sending the application.