No, The aircraft must be certified as meeting the minimum ICAO standards and be certified as such. EASA is not a state. If you wish to fly through any country in a sub ICAO aircraft you must first gain permission from each state. An example are aeroplanes registered as Microlites. The same applies to the pilots licence which cannot be sub ICAO without first gaining permission. EASA takes no part in the process.
The state of registry decides who may fly the aeroplane in accordance with the ICAO agreements. This is irrespective of the residency of the pilot.