Not to my knowledge, they were well past the prime that we think of them in. They had gone through many reforms and become much more political by the point that Roman came knocking.

Try Hellenistic and Roman Sparta by Cartledge and Spawforth, if you are really interested.

They were well past their prime and what you think of as 'The Spartans' didn't really survive the Classical period. After the Sparta won the Peloponnesian war they stretched them selves to thin trying to rule Greece and fight Persia. They would go through a demographic and economic collapse after a series of defeats by Epaminondas and Thebes. Who then dismantled of the Peloponnesian league and freed the helots, the slave class of the Spartans, and built them new cities with modern walls. These cities were near impregnable due to the state of seige warfare and weapons at the time. This severed the Spartans from the free labour that they relied on to support their military state.

During the Roman era the Spartans put on distorted versions of their old rituals and rites of passage for the entertainment of the Roman ruling class.

This is not to say that Spartans didn't serve in the Roman legions or auxiliary units. Though I seem to remember that they may have had a special exemption, but I'd need to look at sources to confirm.

Source: my history of Sparta course in uni.

The text books we used were:

P. Cartledge, Sparta and Lakonia: A Regional History 1300 to 362 BC, 2nd ed. (Routledge, 2002).

M. Whitby (ed.), Sparta (Routledge, 2002).