UniFi APs can run by themselves without the controller unless features like guest portal is enabled (as UniFi controller also functions as a captive portal). Restarting the controller won't restart your APs.
The controller is not required if you are only using "Guest Policy" with "Guest Portal" disabled.
Guest Policy = traffic shaping, client isolation via restricted subnets and Guest Portal (if enabled)
Guest Portal = the captive portal/landing page