I don't know about affecting the application but from reading on here it shouldn't be a problem. As for the parental leave, his employer CAN'T ask him to quit after 4 weeks, it is not up to the employer to decide how much time he can get on parental leave. Parental leave is a part of the EI (Employment Insurance) system in Canada so he will get approximately 60% of his normal salary up to the max limit. His employer pays nothing. Your spouse is entitled to the length of leave based on a number of factors and is guaranteed his job when his leave is finished. Biggest is the number of weeks he has worked in the last year. I assume his employer is not a big company because they would not try to do that. Have a look at this site, should tell you everything you and he needs to know.
https://www.canada.ca/en/employment-social-development/programs/ei/ei-list/reports/maternity-parental.html#h2.2
This appears to be another case of a not honest employer trying to take advantage of immigrants who don't know their rights and the appropriate laws in Canada. Final comment is, his employer can't fire him now since he has already made it known that he plans to take the leave, a dishonest employer might try to do that too.
Hope you get it sorted out, Cheers.