As I understand it, no you will not, unless your carrier specifically supports roaming on other CDMA networks and you opt for that in your contract with them.
So, for example here in the USA, buying a 4S with AT&T is going to get one a GSM enabled iPhone 4S carrier locked to AT&T and with the CDMA radio disabled.
Buying a Verizon 4S and specifically opting for the "global phone" option when ordering, will get one a 4S that is carrier locked to Verizon but will be capable of international roaming on both CDMA and GSM networks using a SIM card provided by Verizon. Rates will be then based on Verizon's various international roaming rates.
In Canada, I have no idea how different carriers will handle it, but as to which radio(s) are enabled and the circumstances of use, that does seem to be carrier-dependent. If your carrier supports both radios and some kind of roaming arrangement, you may be able to do what you suggest. But it would depend on the carrier.
P.S. note that while Verizons global phone option does let an iPhone 4S roam on GSM networks in foreign countries, the roaming rates per minute are quite high. And the Verizon SIM only enables international roaming, so you cannot connect to, say AT&T's GSM network while in the USA.