Is implication(function) more fundamental than lets say conjunction(product) in type theory?

Question

According to the answer at (How to define function type in AGDA) the function type is kind of a fundamental thing in Agda and needed for bootstrapping, hence end user can not define it like what they do for conjunction(product) type and has to be predefined at the language level. Does this mean that implication(function) type is more fundamental than types like product(conjunction) since function is used in defining those types?