Hi Jennifer,
After doing some more investigation into this issue, what you are seeing is the expected behaviour. The "Unable to connect - Position source access error" is a system error, not an alert. Changing the Alert settings in the app menu for each internal or external position source, will only apply to alerts and warning, not system error messages.
Some changes were made in 3.6 beta to ensure this message does not appear when location services is enabled on the device and gets reported falsely on start-up, this is now resolved. But in your case you are seeing this message as expected.
As all feature collected with Survey123 require a location (geometry is required) if you disable the Survey123 app from having access to the position source (location services on the device) you will always see this system error, this is expected and correct behaviour.
Phil.