I could see them amping up Spartan imagery.
I don't know, early on greek identity was mostly based around orthdox christianity and the world of ancient greece was just being rediscovered. This could set the precedent for a national mythology linking the hostility between the nascent greece and the ottoman empire with the war between Sparta and the Persian Empire, with thermopilas serving as analogy of the trenches in ttl WW1 scenario. But honestly is not like greek national mythos excludes either sparta or athens from the pantheon, altho athens gets a lot more of coverage because they had a lot more of influence in what we know and understand about ancient greece and a far more lasting legacy. Sparta was just a slavery based society with a warrior nobility, not unlike may others in the mediterranean and near east.
Honestly the Eastern Roman Empire was far more relevant to who the greeks were in the early 19th century then ancient greece but the later was far more popular for the romatic nationalism of the era.