Well, I’ve never read of such a hypothetical actually taking place. I don’t know what would happen in that case. If Billy has had opposed the MTC based on the fact that the trial court had issued a ruling in his favor, and he would be prejudiced by further proceedings, gopher court might rule in his favor. However, if one does not respond, I don’t know what the court would do when it came time to confirm an award. It could very well say “You got the notice. You knew about it. You snooze, you lose.” I don’t know.
Retraxit is nothing more than a voluntarily dismissal with prejudice. “Voluntarily dismissal with prejudice” is the more common term. As I previously stated, it would help to know a timeline and what was stated in the motion.
When they filed the motion to dismiss with prejudice.
My reasoning is based on the modern law interpretations of the effect of filing such a motion (as explained in the previously linked pdf), combined with the common law definition of retraxit, some of which has been incorporated into modern civil jurisprudence.
Consider the follow hypothetical:
1. PRA brings claims against Billy in az justice court.
2. Billy prevails at bench trial in az justice court.
3. PRA doesn't appeal to az superior court within the time allowed, but instead files a case for the same claims in arbitration.
4. Billy ignores all of the correspondence from the arbitration forum, believing that the court adjudication was final.
5. PRA could file its own "MTC arbitration" in order to get Billy to participate in the arbitration proceedings, but since PRA has paid all of the arbitration costs, the arbitration forum allows PRA to proceed with the arbitration case against Billy in absentia.
The arbitration is held without Billy being present, and the arbiter issues an award against Billy.
As you've said, "The dismissal does not deprive the court of jurisdiction to confirm an award":
If Billy were to oppose confirmation of the award, would "waiver" be the sole basis that Billy could use in opposition of the award being confirmed?