To add:
Between individuals or groups they can be agreed upon. Once principles are agreed upon derivation (or the proof/disproof) of propositions is both a form of research and can be part of empirical research into the way people live up to, form or break their own ethical beliefs.
In short, any empirical research into ethics would require derivation and analysis. So, yes, there is a relation.
I don't agree with you that the subjective axioms need be considered "imagined" or otherwise unimportant. Obviously agreed upon principles are generally one ingredient in creating societies.Sure you can use deduction based on imagined axioms. This has little to do with empirical research.
Between individuals or groups they can be agreed upon. Once principles are agreed upon derivation (or the proof/disproof) of propositions is both a form of research and can be part of empirical research into the way people live up to, form or break their own ethical beliefs.
In short, any empirical research into ethics would require derivation and analysis. So, yes, there is a relation.