Well it doesn't help that we have an open border with them. Even with the "closure" of the border. So yes it does make some difference.
The influence politically and socially that the US has should not be diminished either. You can find proud Trump supporters in Canada. That poisons the ability to be our own country with our own response.
Unrelated I will also say that vaccines are not likely to eradicate the disease... what they will do is prevent people from dying or getting extremely sick, and make it more like colds and flus we already deal with.