A few months at the very least. It may take another month just to arrange the first meeting because unlike Greer, other people have jobs, lives, or better shit to do and a busier schedule. After that it's a matter of how much Greer tries to stonewall the process. He can't draw it out forever by dragging his heels like he has done in court, but he can still make it take longer just be scheduling future meeting dates as far into the future as he can get away with.
A good barometer might be the last time Greer wound up in arbitration, when he tried suing AGT (Freemantle Productions) and the judge kicked the case to arbitration on August 18, 2022 (see the
courtlistener page for the case), but there's no information about how long that took to conclude or that Greer even participated in the process. He tried to appeal the judge's order and that was denied almost immediately. Beyond that, there's not much information available on how long the arbitration process lasted.
This case doesn't seem particularly complicated and Greer isn't likable or convincing enough to overcome his lack of evidence or the evidence that Viatron will bring against his claim. If he refuses to participate in the process he'll wind up losing and stuck with the costs eventually anyways.