It should because PTO runs in the cloud and is more dependent on the browser you use.  If you want to take this to the extreme, you can even prepare tax return on your phone's browser.  FWIW, the recommended system requirements are listed here: https://accountants-community.intuit.com/articles/1861899-system-requirements-for-proconnect-tax-onl...

Having said that, you should NOT use Windows 7 after EOL for your practice regardless because you are still bound by FTC's Safeguards Rule and you may already be in breach of your legal obligations by continuing to use Windows 7 after EOL, at least without ESU, due to potential security risks.  In case you are not aware, you are required to sign off on the following in your 2020 PTIN application:

As a paid tax return preparer, I am aware of my legal obligation to have a data security plan and to provide data and system security protections for all taxpayer information. Check the box to confirm you are aware of this responsibility.