No because you can only apply when you have proof of a job that will last at least 6 months. Once you have that there is a 3 month wait period. Examples of what needs to be in the letter is listed on the forum on one of the posts.
You should get covered using a private health insurance until OHIP kicks in. You can give it a try at Service Ontario. If you are lucky, they may enrol you in. It has happened to a few who I know.