Employer might call to the AINP office, usually nobody does that because employers don't care and it's not their responsibility to notify AINP.
In any case, will your employer call or not, you need to have a solid ground. It means, when you leave your current job, you must already have a new job with the same NOC. Do not quit your job before you sign a new job offer!
For example after your quit, your old employer will make a call and AINP officer decide to start an investigation. He will call you or send an email about your current job. In this case you just send him back a new contract with a new employer and everything will be great. He might also check you linkedin account and call your new employer to verify that everything legit.
If AINP officer will contact, try to be professional and calm, don't throw sh*t on your old boss. I know your are probably want to quit right now and find a new job later, but in this case it would be really easy to lose your nomination. Hang in there. You already went through a lot, it's almost done now.