Yes, and to a very large extent. The Roman imperial army only arose from the reforms of Gaius Marius, which was necessitated by a growing number of Roman landless citizens. Recognizing this, Marius abolished all property requirements and standardized equipment for the army.

But, there is also social and political factors in the empire that markedly changed the armies. As the borders for the Roman Empire solidified, legions became permanently stationed at the provinces which they protect. As time went on, the legions began to recruit from their provinces and adopt their provincial customs. This had two effect. One, it meant that the legions would defend their provinces more fervently, since they were raised and born in that province. However, it also meant that the legions were more reticent about being transferred to another frontier.

Politically, there were many factors as well. If there was a particularly weak emperor on the throne, the army might get a significant donative(a gift of money) in order to ensure their loyalty. Some emperors, notably the Severan emperors, lavished the army with gifts and benefits, leading to a lack of discipline in the ranks that would contribute to the Third Century Crisis. One other political factor was the Constitutio Antoniniana, or the Edict of Caracalla. This granted Roman citizenship for all male non-slaves within the empire, allowing all males to be recruitable. While this is up to some debate, some historians theorize that this led to a degradation of the Roman army, as less appetizing members of society entered the army.

There are plenty of other ways social and political changes affected the imperial army, but these are some of the large ones.

Sources:

Cowan, R., & McBride, A. (2003). Roman Legionary: 58 BC-AD 69. Oxford, UK: Osprey.

Rodgers, N., & Dodge, H. (2006). Roman empire. Lorenz Books.

Parker, G. (Ed.). (2005). The Cambridge history of warfare. Cambridge University Press.