Yes, EE will ask SEVERAL questions, and each question has its own field to select an answer from. So .....LMIA question field is different than the job offer question field, job location, age and so on... This means that the EE system can actually categories candidate based on several and many many ways: For example: selected candidates based on 1) french language test level, 2) job offer, 3) job offer but in British Columbia, 4) LMIA job offer in Alberta, 5) job offer and female and younger than 27 years old, .............etc. This is how Ontario will select you, they will search for people who are in the pool who have a job offer IN Ontario (so they'll use 2 parameters here, location & job offer marked as "Yes"). This will bring OINP to you!
EE requires LMIA if you want to be invited directly from EE using an LMIA supported job offer, (BUT even with that... this LMIA arrangement will only grant you 50-200 points max). source:
https://www.canadavisa.com/labour-market-impact-assessment-for-express-entry.html
However, when you have a NOI, and later, a nomination certificate from a province (after you're done with all OINP paper work), you will be granted straight 600 points. You still need to upload this certificate to your EE profile to be eligible for the 600 points bonus. Once you do so, this means you will be eligible for ITA the nearest EE round of invitation. After ITA from EE, it shouldn't take you more than 6 months, so all in all is roughly 12 months.