I am not sure how you came up with the idea that an appeal is possible under the ICSID rules. In fact, as in most arbitrations, no appeal is possible. This is one of the distinct advantages of almost all, if not all, arbitrations.

ICSID Article 53 specifically provides that no appeal is possible:

(1) The award shall be binding on the parties and shall not be subject
to any appeal or to any other remedy except those provided for in
this Convention."

In arbitrations where there is no appeal, there is almost always, however, a provision, for settjng aside the award where there exists some form of conduct that would make the award fundamentally unfair, for example, where the arbitrators were corrupt (i.e. took bribes). So too in ICSIS proceedings there is such a provision and it is called "annumment", but the grounds for annulment are extermely limited and very rarely alleged. Article 52 provides for an annulment of the award where one of the following exist:

(a) *** the Tribunal was not properly constituted;
(b) *** the Tribunal has manifestly exceeded its powers;
(c) *** there was corruption on the part of a member of
the Tribunal;
(d) *** there has been a serious departure from a fundamental
rule of procedure; or
(e) *** the award has failed to state the reasons on which it
is based.

Without going in to detail, suffice it to say that these grounds are extremely limited and very narrowly interpreted. I would estimate that there have been virtually no, if no, annulments in ICSID history.