Well im inclined to believe that it would play out similarly to the Macedonians; they would likely embrace greek culture and hellenize the territory they conquer, but would still be viewed as half civilized by 'proper' greeks.
What would be interesting is if they unite Greece before Persia comes into the picture.
We’re not sure if Macedonian was a Greek dialect with a heavy substrate or a closely related language. In contrast, Thracian is quite obviously not a Greek dialect and unlike Phrygian, is demonstrably not even in the same family on the larger Indo-European tree, unless we are to accept Thracian, Dacian, Illyrian and Dardanian/Albanian as being a separate branch of the larger Graeco-Aryan grouping... which they likely are, but that would also include Armenian and Indo-Iranian, so yeah. Thracian is not really very close to Greek at all, whereas Macedonian appears to have been. Numismatic evidence from Thrace and Bithynia tells us that the Thracian language was alive and well, even during the Hellenistic Period.
The Thracian will likely “Hellenize” in a similar manner then to the Pontians, Cappadocians, and Armenians, adopting many aspects of Hellenistic architecture and dress while blending the latter with their own, and they will use Greek in their coinage alongside Thracian and speak it at court, much the same way the English spoke French, but the core will remain Thracian. Furthermore, Thracian religion appears to have been very different from Greek religion, and appears to have had a pronounced influence on the latter. There would likely be syncretism, but an all out replacement of the Thracian language, culture and religion I see as highly unlikely.
Also, there doesn’t appear to have been any debate in antiquity as to their Hellenism (they were NOT considered Hellenes), and so I doubt they would be able to unite Greece. An excellent opportunity for them to gain a profitable foothold there though would be during the Peloponnesian War, when they invaded Macedonia. If they can successfully conquer and hold Macedonia, then they gain control of the gold mines at Amphipolis and particularly agriculturally productive area that was famed for its horses. If they can take the highlands of Lyncestis then they can perhaps partner up with or subjugate the Dardanians and the Southern Illyrian tribes (both of whom are relatively disorderly and disorganized and disorderly at this point) to establish an over land trade route with Italy. This would be an excellent way to bypass the wealthy Greek city states and get rich while they tear each other to pieces. If the Odrysians can hold it together in this time, then they can come in and mop up the mess 60 years later the way Philip did.
I’m not entirely sure the Thracians would have the same burning desire for vengeance against the Persians, though. If so, I don’t see them expanding nearly as far as Alexander did, but that isn’t for lack of confidence in their capabilities as they were more or less on par with Macedonia socioeconomically, but rather because Alexander’s conquests if they had not happened IOTL would be considered to be cartoonish and ASB. It might be much more profitable to focus on Europe, particularly gaining control of at least Macedon, Thessaly, Epirus and Southern Illyria, subjugating but not “uniting” Greece and then perhaps expanding into Italy.
They would probably meet the same fate as did the Galatian Celts, Luwians, Phrygians, Lydians, and other ancient peoples of the Asia Minor who later assimilated into the Greeks.
Why? All of these peoples retained distinct ethnic identities for hundreds of years under Greek/Roman rule. We are talking about an independent, Thracian Empire centered in Thrace.