Update Feb 4, 2020: An update for the Pro version is now available (change log).
Yes. The Instagram Feed plugin has already started supporting the new graph API for users that have a business account on Instagram. The new Instagram Basic Display API will also be available to users with personal Instagram accounts before the March 2, 2020 deprecation. We are currently working on an update that will allow existing accounts to migrate to the new Basic Display API. Please see here for more information about the changes.