The crest and motto appearing on your ancestor's notepaper is only part of the Coat of Arms of the Earls of Gosford. The rooster perched on the trumpet is just the very top of the crest.
That in itself does not prove any relationship to them.
If you can get access to a copy of Burkes Peerage 1979 or previous editions you might pick up your George Acheson if he is related.
Burkes is not and never has been a complete record of all family members of aristocratic lines, as usually the contributions are or have been submitted by the Head of the family at a specific time. Intentional omissions are not unknown and there also factual errors.