It has been reported that electron-rotation coupling plays a significant role in diatomic nuclear dynamics induced by intense VUV pulses [Phys. Rev. A 102 (2020) 033114; Phys. Rev. Res. 2 (2020) 043348]. As a further step, we present here investigations of the electron-rotation coupling effect in the presence of Auger decay channel for core-excited molecules, based on theoretical modeling of the total electron yield (TEY), resonant Auger scattering (RAS) and x-ray absorption spectra (XAS) for two showcases of CO and CH++ molecules excited by resonant intense x-ray pulses. The Wigner D-functions and the universal transition dipole operators are introduced to include the electron-rotation coupling for the core-excitation process. It is shown that with the pulse intensity up to 1016W/cm21016W/cm2, no sufficient influence of the electron-rotation coupling on the TEY and RAS spectra can be observed. This can be explained by a suppression of the induced electron-rotation dynamics due to the fast Auger decay channel, which does not allow for effective Rabi cycling even at extreme field intensities, contrary to transitions in optical or VUV range. For the case of XAS, however, relative errors of about 10% and 30% are observed for the case of CO and CH++, respectively, when the electron-rotation coupling is neglected. It is concluded that conventional treatment of the photoexcitation, neglecting the electron-rotation coupling, can be safely and efficiently employed to study dynamics at the x-ray transitions by means of electron emission spectroscopy, yet the approximation breaks down for nonlinear processes as stimulated emission, especially for systems with light atoms.