Note that "operationalization" implies a fairly specific set of epistimolgical and ontological approaches which do not necessarily require that what is being measured has a one-to-one correspondence to a 'real' entity.
Indeed. You can operationally define anything you want within your model. If done carefully, a good operational definition may simplify your model quite a bit. (A bad operational definition, on the other hand, will almost certainly make your model overly complex and can be quite detrimental).
When you use your model to infer about a real world phenomena you have to be careful how you treat your operational definition. If you use it to make prediction, you cannot make a claim that what your operand caused it, not until you go into the real world and find it. If your model is successful you may use your operand to describe your prediction, but you have to justify why your operand is necessary, a better model may exist which doesn’t use an operand at all.
A successful model is neither a sufficient nor necessary condition for proving an operand exists.
