Archimedean specialization of Shelah's conjecture for NIP real fields

Let $K$ be an NIP real field, and suppose that $K$ admits at least one archimedean ordering.

Archimedean specialization of Shelah's conjecture. Then $K$ is real closed.

This is presented as a further specialization of the preceding conjecture: any henselian valuation on a real field is convex with respect to every ordering, so an archimedean ordering forces such a valuation to be trivial. The source does not specify whether this conjectural specialization has been resolved.