Sure, and it wouldn't even have to be like ODST.
I think that if there were to ever be a Halo game in the open world role-playing game genre (probably outsourced to another developer), a non-Spartan character would have the most potential as a main character for two main reasons.
1: RPGs are largely about getting stronger and collecting better gear, and Spartans start at the top in both categories, whereas a base-line human has huge potential for advancing skills and gear, and can even have different starting skills depending on what their professions were in their backstory.
2: Spartans are a highly regulated resource for the UNSC, whereas base-line humans are plentiful and easily get their own branching story without significantly affecting other Halo stories relating to Spartans.
Consider this: You create your character, a low-ranking officer on a zero-prestige ship that's tasked with mapping unexplored regions of space. When passing near what appears to be a normal planet, the ship suddenly lurches and begins descending rapidly. Unknown to the crew, a malfunctioning Forerunner Shield World is trying to pull the ship into the Shield World's interior, only the door is stuck closed, so the ship is going to be smashed into it. This could be the introductory cutscene. There could also be an introductory level about getting to a Pelican to evacuate before the ship smashes down.
After the ship is smashed into the artificial planet, the surviving crew consolidates their forces into what becomes Basecamp Alpha. You are then freed to go questing, and your decisions can affect relations with camps from other ships.
One may be Insurrectionists who are suspicious of the UNSC, but depending on what you do, might be willing to ally with your camp for protection from hostile aliens.
Another might be a camp of Grunts that fled their original camp when the Brutes decided to start eating them, so you can ally with them if you wipe out the Brutes at their base camp.
There's a lot of variety and opportunity for a game like this, and I'm sure game developers would come up with far more ideas than I have.