It might be more training than you actually think, or hope it will be.
Whilst they have combined the 365 and 155 into the Dauphin family with regard to the actual type rating, the differences training required is basically the same, if not more, than that required for an initial type rating!
Have a look at the OEB from EASA:
http://easa.europa.eu/system/files/d...2-08022012.pdf
It is quite a long document, but the tables towards the bottom of it show the suggested training between the different 365 variants and the 155.
From a 365 N2, they suggest 30hrs ground school, plus the ground exam, followed by 3hrs VFR, and appropriate hours for IFR. Then the PC. So a type rating course!!
Good luck.
So back to the question; you cannot log time as you are not rated on that variant. So are not operating crew.