It is inspired to some extent by greek yes, and the way spartan life was for young children definitely compares to the spartans.
I'm a history nerd, especially when it comes to Greek or Roman and midevil times (but I am a Roman history primary and I even play the Rome total war games 👍😁).
Real life Spartan children were taken from their parents by age 7, sent to a military education school and put through intense lessons for a kid to be put through. Around age 16 they were elevated to a higher up military School where they were pretty much getting ready to officially become a soldier. They never live with their parents again once they're taken, and if you marry or fall in love with a woman you couldn't live together till your 30s, and such. Sparta was a very intense military force in ancient Greece and the way their soldiers were raised and trained is what made them so effective.
I can't talk to much strategy wise as Spartans in halo don't fight in formations like the real life greek Spartans did (the Phalanx being the most famous formation for Hoplite/Pike soldiers to use). That said both were thrown into the wilds to survive on their own, all to help toughen them mentally. Greek Spartans actually killed Helotes (slaves) that'd wonder out as a way for food and to actually help keep their slave population in check (the more slaves you have the more chance of a rebellion happens as no one likes to be a slave).
As for your reference to Rome: all I can say to that is a definitive no because the way the UNSC operates is drastically different. The UNSC is more on colonization and self defense, Rome to it's very core was a war machine built off conquering and subjugating you into their empire. Rome was a very invasive empire during it's time, and it's partly why it was so successful because it ran off conquest economically and politically war campaigns was how you went up in status. I don't think anyone would see the UNSC being akin to how Rome was, barbarians hated Rome because you were either enslaved or forced to join their Auxiliary (the Auxiliary being Rome forcing you to join their military, they'd train and give you the equipment though). Rome's downfall can be attributed to various things as well, bad emperor's, a corrupt Senate, expanding to much for their own good that man power and resources started becoming to much to manage. Rome at it's peak is one of the largest empires In history covering almost all of Europe, northern Africa and going as far into Asia Minor.
Anyway, getting a little carried away. The barbarians fought back against Rome not because they didn't think Rome was hmmm good enough to own or responsible enough have the power they had but because they were literally fighting to hold onto their very own freedom. The difference here being the banished aren't fighting for their own freedom the way the Rome's enemies were. If you was a "barbarian", it was either fight back before Rome came to your door step or let Rome waltz in and subject you. This is where Rome holds that title as an Invasive empire and if we know anything it's that invasive empires aren't good (Nazi Germany, Nepolean of France when France attempted to "conquer the world", etc etc .The UNSC isn't like that and they just can't be compared to Rome because of that, colonization uninhabited worlds is miles different to forcibly taking land and massively murdering various people the way Rome did.