No - most Asian nations did not recognize the South Vietnam govt propped up by Western powers. India for example supported Vietnamese independence from the French and recognized the PRG - Provisional Revolutionary Government which was the resistance movement in South Vietnam.
At any rate, even the US vetoed Vietnamese membership to the UN in 1975 - after losing the War.
Only because Jimmy Carter got elected in 1976 on the basis of a campaign pledge to forgive all draft evaders and beat Ford. Until he was elected, Vietnam was three times blocked from admission by United States vetoes in the Security Council.
Solely due to a soviet veto. Most countries recognized it anyway.