@Stevo_M 

The controller really should be online all the time if honest, it is required to handle roaming, AI and Load Balancing.   Running this on a PC that is going to go up and down isnt the best option if honest.

In theory, the AP should remain broadcasting its SSID after the controller goes offline, it will hold its basic settings and any authenticated clients.. but you will lose a LOT of the features.

Remember that Managed EAPs are almost dumb devices, they require the controller to be online to do the heavy lifting.  If you are going to keep shutting down the controller it would be best to either invest in an OC200 hardware controller  OR switch the APs to standalone, however standalone will remove some features.