Well if that's the case, then how will IRCC verify that the applicant is telling the truth and intends to apply for a position in the armed forces? (I'm not doubting the OPs intention to join the armed forces, I'm just stating a discussion, that's all).Incorrect. Every CAF job requires Canadian citizenship and it is written in bold in every job description/position CAF publishes. You will not be able to make it to the interview stage if you do not hold citizenship and have not lived in Canada for the last 10 years, and IRCC is well aware of this.
https://forces.ca/en/help-centre/#/view/14
The reason I'm asking is I have not seen one report on the forum where the applicant was granted Urgent processing without a printed job offer from the employer based on the intention to apply for a certain job.As part of our basic eligibility requirements, only Canadian citizens are eligible to apply for employment within the Canadian Armed Forces (CAF). This means that, at this time, permanent resident status does not qualify you for employment with the CAF.
If you are currently going through the process of obtaining citizenship, you must wait for that process to be complete prior to submitting your application. There is no mandatory minimum time required to possess Canadian citizenship however, which means that as soon as you receive your official citizenship documents, you can submit an application to the CAF.
Also, looks like the OP can apply as soon as the citizenship is granted without having to wait any period of time.