Of course not. Sooner or later, the "reality test" must be engaged.
Evidently Rosen proposes a direct correspondence exists between the structures of mathematics and the real world. As Einstein did, by the way.
We all know how fruitful that presupposition was to Einstein even though it took many years before proper experiments could be framed and finally tested. Which, when they could finally be performed, showed that Einstein's theory was correct.
When does Rosen propose to engage the "reality test"?