can I set up the AP's to work on local mode and then switch to FlexConnect when they connect to the remote WLC?
NO, It won't work like that. You have to set AP mode either to Local or FlexConnect.
Should I use FlexConnect even locally so that the AP's go to the remote WLC and nothing changes?
If you use FlexConnect mode if WLC is not reachable AP goes into standalone mode. I think what you should do is deploy AP in local mode with HA configured in each AP to pointing primary as branch WLC & secondary as HQ-WLC. Only drawback is when branch WLC is down traffic is tunnel back to HQ & you have to similar SSID configuration settings in both HQ & Branch.
HTH
Rasika
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