Answer: Yes and They Already Have!
Review of Safety Reports Involving Electronic Flight Bags
U.S. Department of Transportation Research and Special Programs Administration John A. Volpe National Transportation Systems Center
From a ground operations perspective support for and operational involvement with EFBs is growing yet the training required of them by European aviation regulators is non existent.
There has already been one incident where the assistance of ground operations staff in the computation of take off performance came close to causing an accident to an airliner. So where are all the checks and whistles as far as a piece of equipment that has air safety critical consequences is concerned? Well EASA AMC 20-25 is one place to start but does this document detail essential training for ground staff that are involved with the operational support of the EFB? No; Paragraph 7.12 details flight crew training but nothing for Ground Operations and yet they are often required to provide operational support the EFB especially out of hours and especially where the failure of the EFB could compromise on time performance.
It must be time whereby EASA rethink their regulatory policy with regards to Ground Operations (starting by changing the title - it is most confusing and most misunderstand it) and formalise the regulation of it on a similar style to that of the FAA.