I bought the JA University template some years back, and am now contemplating implementing it. Will it function on Joomla 4?
Yes, there is a Joomla 4 version available.
You can always check to see if a version is available by going to the downloads section. While you will not be able to download without a valid subscription, you can see all the current versions - https://www.joomlart.com/member/downloads/joomlart/joomla-templates/ja-university/ja-university-joomla-4