There is a CP of a company operating High capacity Jets (in Aus) that is not endorsed on type nor does he have 1 hr jet command (or F/O time for that matter), so I guess the answer to your question is NO.
It depends on what you call a "Chief Pilot". My understanding is that "whatever the head of your flying operation is called" doesn't need to be current, but someone in the organisation must have responsibility for the CAR 217 organisation aka the "Chief Pilot". This could be the Head of Training and Checking.