Sparta had been in decline long before the Romans came to Greece. Sparta's height of power was in the 5th century BC. During the 4th century BC Sparta lost much of it's relevance; it was the only Greek city not siding with (or forced to side with) Alexander the Great in his campaign against the Persians in the late 4th century. Sparta was just capable enough to withstand Macedonian pressure, but it wasn't nearly powerful enough to be a threat to Alexander or his Greek allies (indeed Sparta had lost a major battle against Greek forces a few years earlier).
It is more than a century after that that we first see real Roman involvement in Greece. During the First Macedonian War Rome sought the help of the Aetolian League, granting the rights of amicitia (friendship) to the Aetolian League and any city state helping Rome in the war against Philip V of Macedon (Rome was at the same time fighting the Second Punic War, so it had limited resources available for the war in against Philip V). Sparta sided with Rome in this war, and so became an amicus of Rome.
Being an amicus was somewhat short of being an ally; it was certainly not a defensive pact and dit not guarantee any protection from Rome. So it happened that Sparta in 201 attacked Messene, another amicus of Rome, and in 198 - during the Second Macedonian War - Sparta made peace with Macedon even though Rome remained at war with them. Pragmatic as always, the Roman Senate revived the amicitia with Sparta the next year, under condition that Sparta would assist in the conflict.
At the end of the conflict, Rome threw Sparta's actions back in their face. Livy reports that the Romans said this to Nabis, the Spartan ruler:
Though you were our ally you seized by force a city in alliance with us, namely Messene, which had been admitted to our friendship and enjoyed precisely the same privileges as Lacedaemon. And further, you not only concluded an alliance with Philip, our enemy, but you actually established a relationship with him through Philocles, one of his viceroys. In open hostility to us, you infested the sea round Malea with your piratical barques, and have seized and put to death almost more Roman citizens than Philip, so that our transports, which were supplying our armies, found coasting along the Macedonian shores safer than rounding the Cape of Malea. Forbear henceforth, if you please, to talk about your loyal observance of treaties; drop the language of a citizen and speak as a tyrant and an enemy. (Livy 34.32)
As Rome had given many Greek cities their liberty by defeating Philip V of Macedon, so too would they give liberty to the city of Argos, which was under Spartan occupation. Under this pretext Sparta was defeated by Roman and Greek forces, ending whatever remained of the Spartan hegemony in Greece. Sparta was forced to join the Achaean League.
For the next fifty years or so Rome remained involved in Greece while proclaiming that the Greek cities were free. During the Third Macedonian War (171 – 168 BC) Rome took prominent members of Greek communities as hostages to Rome, to ensure the continued loyalty of the "free" Greek cities. Eventually, after the final defeat of Macedon in 148 and the incorporation of Macedon in the Roman empire, it came to war between Rome and the Achaean League. The catalyst, interestingly, was Sparta.
Since Sparta was forced into the league, it continuously tried to leave the league. At least three times the Spartans or Spartan exiles petitioned Rome with challenges tot he jurisdiction of the Achaean League, each petition being counter petitioned by representatives of the league. As Erich Gruen put it:
Senatorial reaction was cast in the traditional mold: evasive and noncomittal answers which each party read in accord to its own wishes and employed to justify steps already determined upon. (p. 520)
Finally Sparta seceded from the league, and the Achaean League responded with force. They figured this was an intra-Greek conflict; the Greeks were nominally free and Rome had so far proven to be mostly indifferent to what happened. Rome responded swiftly and decisively though. Roman forces moved from Macedonia and Italy into Greece and crushed the Achaean League. From then on Greek cities were no longer allowed to form confederations. Some cities - those which had resisted - were put under control of the Roman governer in Macedonia; others, including Sparta, remained "free". It would take another century before this charade was dropped and Greece was made into an official province of Rome. By then the Greek city-states had lost most of their relevance, except perhaps to serve as cultural guides (the Romans of that time loved Greek culture).
To answer your question:
Sparta was no longer conducting military operations at the height of the Roman Empire. It was just another Greek city without much relevance. Spartan forces fought with and against Rome in the third and second century BC, but by the height of the Empire they were pretty much irrelevant. Men from Sparta may have served in the Roman legions or auxiliaries, as men from all over the empire did; but they were not incorporated as a legendary unit or something.
Main source used:
Also interesting (on Roman expansion and its nature):
W.V. Harris, War and Imperialism in Republican Rome 327-70 BC (Oxford 1979)
A.M. Eckstein, Senate and General: Individual Decision-making and Roman Foreign Relations 264-194 BC (Berkeley 1987)
Sparta had lost pre-eminence long before Rome became involved in the Balkans. Sparta had lost its hegemony it won in the Peloponessian war at the Battle of Leuktra in 371 BCE to Thebes, and it never really recovered. By the time Rome entered Greece (shortly after the end of Punic 2 ~202 BCE) the Hellenistic kingdoms were far more important and powerful than what was left of Sparta.