Player election deadline is tomorrow .
I would also be incredibly surprised if he does not file for arbitration. Players almost always do as it's one of the few bargaining chips they have in their favor. There really is no downside for Bratt to file.. even if he wants out, arbitration would be the fastest path towards FA.
Also, to answer the original question posed, arbitration doesn't affect timing towards UFA. It's still 7 accrued seasons or age 26. Bratt has 5 accrued seasons at age 23 so 2 more seasons would get him to UFA. If he elects arbitration, the Devils would have the choice to pick a 1 or 2 year award. They'd likely pick a 1 year award so they can be back in this position next year rather than Bratt having a direct route to UFA.