Currently, a foreign investor cannot sue either the Canadian government or the Quebec government under the ICSID rules, since we are not members of the Convention. Once that is the case, under the mechanism containing the ICSID clause—the clause referring to the dispute resolution mechanism—the answer might be different.
For example, if Quebec implements an act at the provincial level, it asks the federal government to designate it as a constituent subdivision. Then it is possible for the Quebec government to include an ICSID clause in its contracts and for a foreign investor to sue the Quebec government.
In the case of international investment treaties, since treaties are generally in the name of the federal government, only the federal government can be sued.