Not going to happen. It's too far, and the Celts that would be making this trek would be seeing plenty of suitable land to conquer and settle on the way there - why cross more mountains, deserts, rivers, etc. to make it to Persia, specifically, when you could settle Phoenicia or something (assuming they must go past Anatolia, which I don't think there's much reason why they should). Plus, they'd lose a lot of numbers getting there in the first place, and would have difficulty even usurping as populous a land as Persia from such a distance.
Now, as an alternative suggestion for a "barbarian" Persia, the Scythians, provided they have a pretty large wave, could make their way there and settle. After all, they did a pretty good job disrupting the Medes in the early sixth century BC, and had the capacity to do something like this for a long time afterwards.
EDIT: What time are you thinking this takes place? I suppose that makes a difference: I'm thinking post-whenever the Galatians came along (around 280 BC, right?), and I suppose the Galatians could find themselves as mercenaries under the Seleucids and fight in their eastern provinces, and some permanently settle out there, but that's about the extent I see - no mass migration.