Any controller's competency to use the kit is an ongoing issue and subject to scrutiny by your LCE. This can become an issue at any time so is not really connected with an extension board.
If deficiencies are noted during an extension board the procedure would be for the examiners to draw attention of the facts to the LCE who is then responsible for taking appropriate action. Such action would be considered in consultation with the Watch Manager and the controller concerned and might involve additional training if necessary. SRG would, doubtless, maintain an interest in the situation and require some satisfaction regarding the action taken.