No. When a class object is saved, the saveobj method for that class gets called, if it exists. If this method throws an error, it is caught, and thrown as a warning instead. Therefore the best you can do is generate a warning. If you don't want the object to be saved, then you can have the saveobj method return an empty array, which is saved instead:
function a = saveobj(obj)
a = ;
Warning 'myclass objects are unsaveable.'