Exactly, as stated, if you apply for a FULL TIME study permit and then apply for working FULL TIME that is simply not possible. But that is for getting the permits. If the officer issued the permits, then you are entitled to do as you please, they already gave permission.
I think that some facts are missing. I have a work permit and a visitor visa, the reason is my country is required to have a visitor visa regardless of the work permit. The work permits allows me to work here, period. The visitor visa allows me to enter Canada. Two different things, two different papers.
When you enter Canada you are required to provide the permission to enter the country (the VISA) then you are required to prove what you are going to do (work permit, study permit, etc.).