Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation?

The X(3872) is universally accepted to be an exotic hadron. In this letter we assume that the X(3872) is a D0 \bar D0* molecule, as claimed by many authors, and attempt an estimate of its prompt production cross section at Tevatron. A comparison with CDF data allows to draw some qualitative conclusions about this statement.