That is, the parties are quite free to condition their consent to arbitration (e.g. on the claimant having waited a certain amount of time). In this case one could argue that their consent was conditioned on the appointed arbitrators passing the PCA challenge procedure.

The consequence of the successful challenge would be, as you say, not to remove the arbitrator, but rather to preclude the tribunal from hearing the case on jurisdictional grounds. Plus the ICSID challenge procedure would still remain in effect, so a second challenge could be brought under it if desired.

But on this reading, while you are right that the party-selected procedure could not actually remove Judge Breyer, it does not become a nullity.