Let's first clarify that "vasomotor rhinitis (VMR) otherwise known as non-allergic rhinitis" is the non-allergic reaction (NAR), which can be similar in symptoms to the allergic reaction (AR), but not the same.
Vasomotor rhinitis is a poorly understood disorder which mimics many
of the symptoms of nasal allergy, but has a completely different
basis. Failure to recognize these differences has led to a great deal
of misunderstanding about this disorder.
This symptom might be more common in allergic rhinitis (AR), though we can't really be sure, since we don't know how commonly it occurs in everyone else. (It breaks down into a statistics problem which we can only approximate with certain assumptions.)
However, based on this study:
Nonallergic Rhinitis, With a Focus on Vasomotor Rhinitis Clinical Importance, Differential Diagnosis, and Effective Treatment Recommendations
[One survey of US medical practices] suggest that at least 57% of rhinitis
patients have some
contribution from NAR [Nonallergic rhinitis] causing their rhinitis symptoms. Similar
European studies have found that approximately 1 in 4 patients
complaining of nasal symptoms has pure NAR .
So it seems that people often mix up Allergic Rhinitis (AR) and NAR so much, that even many cases of "AR" are actually still just NAR. So maybe people with AR have AR occurances instead of NAR, and NAR to NR ratio is about 1-to-1. However, if we assume that all people have relatively the same number of NAR symptoms, then it seems likely that people with AR have at least slightly higher occurances of this symptom.