So first off, I would say it is likely that you would be able to check the bags as Aegean is usually good about this.
However, if you are not eligible to enter Schengen, then I would really not chance this. What will you do if it is not possible? Throw away the luggage? Not board the flight? You should definitely plan for what you would do if you can not check the bags, as it could really impact the trip.