Yes, loading on the CONF_DONE line can result in Late CONF_DONE assertion or an Early CONF_DONE assertion which will cause configuration failure from your configuration device.
You can use the Program Length Count (PLC) option in Quartus® II software to verify if the error is due to a Late CONF_DONE assertion or an Early CONF_DONE assertion.
To use the PLC option click on File>Convert Programming Files>Advanced Option
Change the PLC adjustment box
1. To a positive value with a step size of 8 if experiencing a Late CONF_DONE error
2. To a negative value with a step size of -8 if experiencing an Early CONF_DONE error