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.
Err.. a puppet state created by France and only recognized by the West. It was never part of the UN and its membership was explicitly denied.