Not currently. It can be worked around somewhat by providing a custom toRepresentation method: 

struct MyStruct {
    int value = 42;
    Json[string] toRepresentation() {
        Json[string] ret;
        if (value != 42) ret["value"] = value;
        return ret;
    }
    static MyStruct fromRepresentation(Json[string] j)
    {
        MyStruct ret;
        if (auto pv = "value" in j)
            ret.value = pv.get!int;
        return ret;
    }
}

As far as I understand I need to implement serialization for whole object in this case?

Instead of the @optional!canSerialize another (or an additional) possibility would be to handle @optional Nullable!int value; in that way.

Doesn't work for string[] for example.

Of course, skipping the value if it equals .init, like suggested in the OP, is also a possibility.

Any further opinions or use cases?

REST server accept only one of two fields and reject request if you send both for example.