Yes, you can apply for a work permit after you receive a nomination certificate from the AINP, so all you need to have is nomination letter, job offer from Alberta employer, plus copies of passport, previous WP if any, fees.
if your work permit will be expired within two weeks and you are in Canada, you can apply work permit extension without an actual LMO. It's called concurrent processing, just includes the LMO file number with your application.
search "Operational Bulletin 152A" on google for details