Not deep, but scratchy. There's few of them about and they are very distinctive once heard, but not always in a good way. Rod is a fine example, listen to the warbling scratchiness in 'In a Broken Dream'.
Those other women you mention are clear-voiced, though distinctive, especially Amy.
I can sense some scratchiness in this Rod song, I'm not so smart though, I hadn't thought about him having a scratchy voice. I guess his voice is so recognisable like you mentioned though. I need to train my ears some more.