No, you can’t use pass-by-reference with the Action delegates. While there is a concept of “type passed by reference” as a Type in the framework, it’s not really a type in the normal sense as far as C# is concerned. ref is a modifier for the parameter, not part of the type name, if you see what I mean.
However, you can build your own set of equivalent types, e.g.
delegate void ActionRef<T>(ref T item);
Of course, if you want a mixture of ref and non-ref parameters in the same delegate, you get into a horrible set of combinations:
delegate void ActionRef1<T1, T2>(ref T1 arg1, T2 arg2);
delegate void ActionRef2<T1, T2>(T1 arg1, ref T2 arg2);
delegate void ActionRef3<T1, T2>(ref T1 arg1, ref T2 arg2);