No. ArcMap is a specific program within the ArcGIS Desktop product. Questions specifically targeted as that are no less relevant/deserving of a tag than the other components (which also have tags): ArcScene, ArcGlobe, and ArcCatalog.
It is useful to be able to follow a tag on the specific application rather than having it merged in with all Desktop questions, though as you point out both tags are applied in the current majority of cases (and an unknown amount of those 'desktop' tags are related directly to the previous discussion in http://meta.gis.stackexchange.com/questions/3131Tagging ArcGIS questions).