Yes. See this article for some information about the treaty making process:
In Canada, the treaty-making process is controlled by the executive branch of the federal government, while the Parliament of Canada (“Parliament”) is often responsible for passing legislation to implement international treaties at the federal level.
Although this entire process is controlled by the executive branch, the federal government does involve Parliament in this stage of the treaty-making process by tabling treaties and relevant explanatory documents for debate in the House of Commons.
So while the executive branch can enter into treaties at will, they can't create or alter domestic laws without legislative approval. For example, if a treaty required that Canada make certain things illegal, then the legislature would have to pass legislation making that thing illegal to make Canada compliant with its treaty obligations.
Approving a new NATO member wouldn't affect domestic law at all, as there is no bill the legislature would need to pass to implement it. It would effect military operations, but the executive branch already has the power to decide military strategy (the King is the commander-in-chief of the military, he delegated those powers to the governor general, and the governor general by convention only acts on the advice of the Cabinet).
Note that unlike many other countries (such as the US), the Canadian constitution is mostly silent on the topic of international treaties, only mentioning treaties agreed to by the UK on behalf of Canada (at the time the constitution was written, Canada couldn't agree to treaties itself), so there are no constitutional requirements for the legislative branch to approve any treaties.
Also note that treaty implementing legislation is almost always passed, since the executive branch needs to maintain the support of a majority of the legislature. If the legislature doesn't pass implementing legislation, then the legislature would also be very likely to pass a no-confidence motion, which would usually trigger a new election.