Yes Honda can recode the immobilizer, but only if this is active in Hondata (ecu) software. If the green key is flashing then it means the imob is not active and they can't recode the immob and also they can't enable the immobiliser through HDS, as far as i know, this can be done only in hondata and for that you need a Kpro, k100 doesn't allow acces in hondata software.