Yes and no. At my workplace, the reference to a work wife is only done with people that have known each other a long time. And it's not in the sense that you put it. For example at my workplace there is Frank and Ashley. Frank and ashley have worked on projects together for years. Often times Ashley has to get on Frank for getting something turned into her. or Frank has to go over the minute details of something with Ashley again. So in some ways it is a relationship with a lot of give-and-take, knowing each other's routines, knowing each other's strengths and weaknesses, and some nagging, like a marriage.
Similar to the "work husband" / "work wife" dynamic at my workplace. Know the person, including quirks, habits, so well that the interactions seem akin to an old married couple at times. There is no manager-subordinate dynamic here though. The "married couple" are peers/at the same level.