Why do you think that it should be enough of a language proof? Where did you read that sending such information is sufficient?
I think they will send your application back, to be honest. All the reasons not to provide IELTS/CELPIP are here -
https://www.canada.ca/en/immigration-refugees-citizenship/services/canadian-citizenship/become-canadian-citizen/eligibility/language-proof.html, and your case is not stated there. Only a diploma/degree of a program taken in English (the diploma/degree must explicitly state it) can be used, but not enrolment in a program.
If I were you, I would immediately book a CELPIP test for your wife, pass it ASAP, and submit via Web Form, so when they finally open your package, there is a chance that they won't send it back, already having your wife's test results electronically.