No, you will not get a confirmation of receipt from CPC-Mississauga. You won't hear from them until they have finished assessment of the sponsor and rendered a decision. The only way to know that your application was received is to ship is via some method that provides a tracking number.
A sponsorship application is not reviewed until they open the package - and the decision is typically made that same day unless there is a complication. So while you are waiting, your application package is not even opened yet. So it won't be entered into their system until the sponsor's decision is made - then you can access online. Typically you need the sponsor's client ID # and, unless the sponsor is a permanent resident, s/he won't have a client ID # until one is assigned when the application is opened.