As the other poster said, the 20 years is you financial liability as the sponsor, nothing to do with health insurance.
As you have said OHIP - I assume they will live in Ontario (as in Ontario Health Insurance Plan) - i.e. you are not mistakenly using the acronym to refer to Canadian medical insurance in general - as it is different province by province (I don't mean to appear to be patronising, just want to answer the question

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Under OHIP, they should 'register' as soon as possible at any Services Ontario office soon after landing for residence in order to 'start the clock' on the three month waiting period. So they would be covered after three months. They must register. Other provinces have no such waiting period (e.g. NOva Scotia). So yes, they would need private health insurance to cover them for the three month gap.
Hope this helps!