This came up in a discord server reference Assassins in a Custodes list, so I will copy/paste my response:

My interpretation is no, even RAW. The custodes page specifies the detachment must only be Custodes to get the benefit. The Agent of the Imperium paragraph says it does not prevent other units in your detachment from benefitting from Detachment benefits. No backwards capability of Detachment benefits from the host detachment to the Assassin is implied or suggested.

I think it's a pretty big leap in logic to go from "this character doesnt prevent a pure detachment from getting detachment benefits" to "he gets the benefits too!"