Obviously considering we're not working with wings with 6% sections, we can go for lighter density foams, but is it possible?
It is possible, but the softer the foam core is, the thicker the skin has to be to give sufficient strength.
I think that you will find that the total weight will be significantly higher than for the foam core/balsa skinned wings. The alternative is to use hollow wings, i.e. sandwich construction.
Regards,
Magne