Hey there. So if you check on the govt of Canada website, you can see the processing time for student visas is 13 weeks right now. So technically, if she applies now, your wife could get approved for a temporary study visa by the time your mom has surgery early next year. Here's the website you can check for processing time:
https://www.canada.ca/en/immigration-refugees-citizenship/services/application/check-processing-times.html
This website also has more info about student visas:
https://www.canada.ca/en/immigration-refugees-citizenship/services/study-canada.html
Remember you'd also have to be careful about crafting a good application for her study visa.
However, I would caution that if her application for a study visa gets rejected, and then you apply for spousal sponsorship right after, that
might raise suspicions about the authenticity of your relationship in your spousal sponsorship application (as in it might look like your wife is just trying to find a way to get into Canada). BUT, please note that this is entirely my guess, and I suggest you call an IRCC agent or perhaps someone more knowledgeable on this forum can comment on whether or not applying for a student visa before spousal sponsorship would in anyway hinder your spousal sponsorship application.
I also think it's possible that this wouldn't negatively impact your application, because after she comes here on a student visa then you could simply apply for spousal sponsorship as an inland applicant after getting married in Canada, and a lot of people already do that...So I know it's possible, but not sure what the effects of these things would be, which is why I would consult someone with legal expertise on the matter.
But I certainly think it's not a good idea to apply for a student visa AFTER submitting your spousal sponsorship application. That could delay your spousal application and raise questions. If you want to try the student visa route, you should figure out if that will work now without negatively impacting your spousal sponsorship application later, and if it doesn't, have your wife apply for the student visa asap. I hope that helps.