Both classes have Tightlock couplers; Wikipedia (I know I know lol) states that multiple working for 323s is limited to within class only in normal service and with other classes when rescue is required or for empty coaching stock moves as you mention. Not being familar with either class, I don't know how often the latter occurs in practice if at all. I'd be interested to know either way, as these unusual unit combos have always fascinated me.
Going back at over a decade ago & to use a far more relevent (for me at least) example of this sort of thing with ScotRail, you could sometimes get a Class 314 working in multiple with a Class 322 on a ECS move from Shields TMD to Glasgow Central (see link below), but they never worked in normal passenger service together.