Probably not. See STCW Convention Regulation V/1-2, paragraph 3:
Masters, chief engineer officers, chief mates, second engineer officers and any person with immediate responsibility for loading, discharging, care in transit, handling of cargo, tank cleaning or other cargo-related operations on liquefied gas tankers shall hold a certificate in advanced training for liquefied gas tanker cargo operations.
The same applies to oil and chemical tankers, see STCW Regulations VI/1-1, paragraphs 3 and 5.
Unless the 3rd Mate is not going to stand a cargo watch and/or not be the person in charge of a cargo operation, they are going to need the advanced STCW endorsement.
James D. Cavo
U.S. Coast Guard
Mariner Credentialing Program
Policy Division (CG-MMC-2)