Speaking for the period of the Sacred Band of Thebes: no, they didn't. Classical Greece did not have special forces in the modern sense. Since state finances were in their infancy, and the resources of Greek city-states were tiny, it was generally not justifiable to invest in military infrastructure or manpower unless there was a clear return in terms of the defence and strategic capabilities of the community. In other words, there was no money for small units of super-specialised professional soldiers. The war budget tended to be spent on ships, fortifications, and wages of troops in the field.

This is not to say that there was no significant military spending, or that there was no troop specialisation. In the 4th century BC (the time of the Sacred Band, which existed c. 378-338 BC), Greek city-states invested heavily in mercenaries, with a particular focus on specialist light infantry. There was a good market for Cretan archers, Thracian peltasts and other experts, who were specifically hired for the skills they possessed. These were used to complement the hoplites and cavalry that the citizen levy produced. The difference between these mercenaries and modern special forces, however, is that they were not small elite units trained for special (covert) operations. They had particular roles to play in the established Greek tactical system, and rounded out existing armies rather than providing them with unique and specific military options. Indeed, Greek city-states also hired mercenary hoplites and cavalry, even when they could already raise their own; Classical Greek mercenaries were a source of additional (and expendable) manpower first, and a source of military specialists second.

Besides mercenaries, Greek states that could afford it also increasingly invested in the first small standing forces. These were composed of citizens, raised as regular militia but paid to stay at the permanent disposal of the state. Their ongoing service was expected to allow them to train for war and provide the general levy, when it was raised, with an experienced and reliable core unit.

The Athenians seem to have pioneered this idea when they set up a force of archers, probably primarily to serve as deck-fighters in the fleet. The archer corps was composed partly of citizens, partly of immigrants and mercenaries. Their use on triremes would have required them to have special skills, as did their weapons - but they were a corps of 1600 by 431 BC, and could hardly be considered a small military elite.

The Athenian cavalry was also state-funded, but wasn't a specialist elite either, being expanded some time around the 440s BC into a force of 1200 horsemen. Unlike the archer corps, the cavalry was citizens-only; it was part military unit and part leisure-class club, and foreigners were not allowed in. Even so, getting the rich to send their sons to join the cavalry required a considerable investment by the Athenian state, which issued loans for the purchase of a horse and paid upkeep for horse and rider.

The investment element is definitely present here; the Athenians were paying upwards of 40 talents annually (the equivalent of 800 yearly wages) for the privilege of having a cavalry. They kept paying for their cavalry corps right the way through the 4th century BC, showing how important they thought it was to have these mounted troops defending Athenian territory. However, the reason for their willingness to invest was precisely that horsemen were not a hyper-specialised elite; they played countless crucial roles in the warfare of the time, and provided essential service in protecting farmland whenever Athenian territory was invaded. They were not special forces, but a very effective and extensively deployed element of the militia army.

The standing units of picked hoplites first raised in other Greek states were worth their cost for similar reasons. Argos was the first to maintain a picked hoplite unit (called the Thousand) at state expense; the Theban Sacred Band is only the most famous example. However, from the track record of the Sacred Band, we can tell that they were specifically not a special elite force intensively trained for covert operations. They fought in a number of different situations, protecting Theban land from enemy invasion, taking the lead in assaults on enemy forces and positions, and fighting in the battle line when the Theban militia was called out for pitched battle. They were worth the investment because they could be applied to a number of common, even typical situations, where the average hoplite militia often fell short. Indeed, several sources stress that one of the main functions of such elite corps was not even military; their purpose was to prop up the existing regime and protect it against treachery from within. The main criteria for recruitment to these standing units, besides physical fitness, was wealth and loyalty.

There are a couple other units that could be discussed under the heading of "something like special forces if you don't look too hard" (the Spartan Krypteia, if we follow a late source describing its duties, or the enigmatic Skiritai), but there was certainly nothing like the modern SAS or Navy SEALs. Apart from the financial argument (hyper-specialised troops were not worth the investment required), this absence is also explained by the fact that modern special forces are elites within a professional military. Since Classical Greece had no professional militaries, it would not make sense for troops to be raised that brought military professionalism to an even higher standard. In the age of the Sacred Band, Greek armies were untrained militias which contained, at best, some mercenaries and a few versatile elite units that could just about be considered professional soldiers.