To collect EI benefits, the individual must have worked 600 hours in the qualifying period (ie the 12 months before the leave starts). And I believe the max duration is 50 weeks, further payment requires another 600 hours of work.

Three consecutive years would involve a significant amount of unpaid time which (I'm going to presume you are American) you Americans are certainly able to take.

Source: Parent of two in Ontario and http://www.esdc.gc.ca/en/ei/maternity_parental/eligibility.p...

Edit: Grammar, clarity