Question: What action should be taken when a pilot is "cleared for approach" while being radar vectored on an unpublished route?
Answer: Remain at last assigned altitude until established on a published route segment.
In Canada, cleared to the approach I would be able to, and probably would get into an untenable position later on the approach if I didn't, immediately descend to the 100 nm or 25 nm safe altitude published on the plate, as appropriate, in preparation for intersecting a published route segment. I would tell ATC I was "leaving one fife tousand for one zero tousand tree hundred" or whatever the sector altitude was, but I'm not sure I'd be required to do that. Saying it helps me remember it, and allows ATC to know what to expect.
I remember being told by a flight instructor long ago that in the US you were not allowed to descend immediately on being cleared for the approach, and commenters here told me that yes you were, but with this question I may have finally found the case that the original flight instructor was considering. It looks like if I'm on an airway or a published transition to an approach, cleared for the approach clears me to the MEA for that route, but if I'm off airway just being vectored towards the airport, I can't descend to a published safe altitude until directed? I suspect this is more because US airspace have more published transitions and routes and less just hammering around through the clag towards the NDB at the airport.