This page from the Government of Canada indicates the two countries are sharing relevant information. So would Canada refuse entry to someone who is banned from the US because of overstaying?
Reasons for inadmissibility
Note: This is only a guide. A Canadian immigration officer will decide if you can enter Canada when you apply for a visa, an Electronic Travel Authorization (eTA), or when you arrive at a port of entry.
A person may be denied a visa, or an Electronic Travel Authorization (eTA), refused entry to, or removed from Canada on any of these grounds:
- security reasons, including
- subversion (attempts to overthrow a government, etc.)
- violence or terrorism, or
- membership in an organization involved in any of these
- human or international rights violations, including
- war crimes
- crimes against humanity
- being a senior official in a government engaged in gross human rights violations or subject to international sanctions
- committing a serious crime that would be punishable by a maximum prison term of at least 10 years in Canada Footnote 1
- having been convicted of a crime, including driving while under the influence of drugs or alcohol Footnote 1
- organized crime, including membership in an organization that takes part in organized criminal activity, people smuggling or money laundering
- health grounds – if their condition is likely to:
- endanger public health or public safety, or
- cause excessive demands on health or social services (some exceptions exist Footnote 2 Footnote 3)
- financial reasons – if they are unable or unwilling to support themselves and their family members
- misrepresentation, which includes providing false information or withholding information directly related to decisions made under the Immigration and Refugee Protection Act (IRPA)
- failure to comply with any provision of IRPA Footnote 4 or
- having an inadmissible family member.
However, the big disclaimer at the top says that this list is just a guide, and that your admissibility depends exclusively on what the immigration officer handling your case decides. In addition, Article 2, paragraph 2 of the agreement you linked specifically says that the two countries share information with the purpose of enforcing immigration laws in their respective countries:
The purpose of this Agreement is to assist in the administration and enforcement of the Parties’ respective immigration laws by:
- using Information in order to enforce or administer the immigration laws of the Parties;
- furthering the prevention, investigation, or punishment of acts that would constitute a crime rendering a National of a Third Country inadmissible or removable under the immigration laws of the Party providing the Information; or
- facilitating the Parties’ adjudication of an application for a visa, admission, or other immigration benefit, or determination of whether an individual is to be ordered removed by providing Information regarding the admissibility of the individual.
This is to say that Canada can inquire, and if so will be informed, about the US ban. You admissibility will therefore depend solely on the immigration officer's decision based on all the information they have. They will know what, when, why, and how you overstayed. It goes without saying that one should not omit this information in one's application.
Now, overstaying in a country is generally a red flag when applying for a visa in another country. A previous overstay in any countries makes you immediately untrustworthy, and casts serious doubts about your intentions of actually leaving Canada. Therefore, the answer to whether being banned in the US renders you inadmissible in Canada is likely to be yes.