I installed Office 2016 recently and got a warning that Sidekick Outlook plugin is not supported. Will this be an issue?
Yes, this is an issue because its functionality will be affected. You need to install the latest version of the plugin which is said to be compatible with the Office 2016.
Remove the previously installed plugin and then access the following page to download it: https://app.getsidekick.com/outlook/download
Reboot the PC and then check the message. It should work properly.