You won't get MSP until at least a few months after you apply for PR. I believe it is getting a bit easier to do it; it used to be a fight with MSP to get coverage before PR.
He most likely won't be able to add you to his benefits as just his girlfriend; you will need legal status as a spouse, either married or common-law. Also, employer benefits generally require provincial health coverage first. If you don't have provincial coverage and his employer says they can add you to the plan, get confirmation from the actual insurance underwriters. If it turns out that the insurer's fine print required provincial coverage and they find out you didn't have it, you would have to pay back any claims you made.