Do spring varietes of cereals have a process of vernalization?
The answer depends to some degree on what you mean by &quot;some process of vernalization&quot;. As far as I know, the difference between winter and spring varieties is a matter mostly of how strong the response is, not whether the response exists.
One paper writes in the abstract:

Wheat cultivars are classified as two general types: winter wheat with variable low temperature requirement for a proper flowering time (vernalization) and spring wheat without the requirement, based on their qualitative vernalization requirement. Winter wheat cultivars are classified as three types, weak winter, semi-winter and strong winter, according to their quantitative vernalization requirement to reach a vernalization saturation point or achieve the maximum vernalization effect.

The difference is not whether vernalization exists as a process, so much as whether it is required for timely reproductive transition.
See the figure below (from this paper), showing spring (LEG) and winter (MIR) varieties of wheat after various vernalization periods. Basically, even the spring variety has a weak vernalization response; it's just much less notable than the strong response of the winter variety.

With legend:

Frost tolerance (LT50), apical development (DC = decimal code) and days to heading of ‘Mironovskaya’ (MIR) winter wheat and ‘Leguan’ (LEG) spring wheat plants during 12 weeks of acclimation at 2 °C and two photoperiods, 16 h (long day) or 8 h (short day). Vertical bars indicate LSD0·05 and asterisks indicate that the plants had not reached heading by 100 d.