Let's say he gets everything together in the next few weeks - IELTS results, education assessments, etc. - any idea how long it takes to make it in a draw and be asked to apply to PR through a provincial nomination? Can your employer apply for a LMIA if you are waiting for an invitation to apply provincially? Is there a way to keep working while you wait for an invitation to apply? Can you apply to stay in Canada as a visitor while you're waiting for the results of a LMIA? What about staying as a visitor while waiting to see if you get a ITA?
Plan on it taking several months to get ECA and IELTS done (a few weeks is unrealistic, especially under COVID-19).
Suggest you spend time reading through the discussions in the PNP section of the forum to understand how provincial draws work. There is going to be no concrete answer to the question of how long it will take to receive an expression of interest from the province.
Employer can apply for an LMIA at any time.
If he wants to keep working while he waits for the expression of interest from the province, then he needs an approved LMIA so that he can apply for a closed work permit.
Yes, he can certainly convert his status to visitor and stop working.