Considering a bunch of Tabula Rasa humans with rocks are capable of building a civilization capable of surviving for years, I give a group of exalts a much better chance.
Artifacts make this even better. The twilight knight's sword is probably one of the best weapons in the game, and a daiklave is night and day better than a mortal sword. Now it's entirely possible the twilight sword is magical, but I really doubt it breaks the properties of momentum.
It really depends on if they get a lantern hoard or not. Solars still need to sleep at some point, and if you keep getting woke up by surprise anticipation method you're going to get really tired of the constant bombardment of monsters. Even if monsters steer clear of anima flare, you can't keep your anima burning forever.
Lunars can just sacred hunt one of the monsters and take its shape. If the various monsters don't hunt one another, this is a solution to the above problem. If they do, not so much.
Dragonbloods are still exalts, and they've still (likely) got artifact weapons and armor, if not more than celestials would. They have the same problems solars do, and while they're individually weaker, I imagine something like Threshing Floor Technique would let a brotherhood simply destroy a King's Man.
TLDR; Depends on if they can find somewhere to sleep safely.