The ability to check a third bag is actually a *A privilege for *G members. UA 1P and 1K members receive this privilege on all *A flights. I assume US will offer this benefit when it officially joins *A.
Premier Executive level members also receive Star Alliance™ Gold benefits when flying on any Star Alliance airline-United, Air Canada, Air New Zealand, ANA, Asiana, Austrian Airlines Group, bmi, Lufthansa, SAS, Singapore Airlines, Spanair Group, THAI and VARIG.
Priority baggage allowance, which may allow one additional checked bag for a total of three on any Star Alliance flight in any class of service
United code-shares with many other airlines, such as Aloha, BWIA, and Air China, which are not members of *A and do not allow a third bag to be checked for free. It is clearly noted that this privilege is only available on flights operated by Star Alliance members.