City of Spokane here. Our window to appeal is very short - you have to do it before you leave the test room. (Scoring corrections and -- perish the thought -- legal challenges are not appeals in that way.)
We would try very hard not to certify the list for hiring until the appeal is resolved. Employees can work "out of class" temporarily. But I'll speculate a scenario where:
(a) a promotion had to be made,
(b) the appeal was later upheld, and
(c) only the order of names was changed (i.e. the entire list was not tossed).
I think our Commission could "fix" the promotional list by making the appellant whole (seniority, salary, etc.) as if they had promoted. The person who did promote but shouldn't have can also be granted laid-off rights to the job class (and could retain seniority for the time actually served).
Again, that's my best guess based on somewhat similar situations. I haven't seen this exact situation happen in my 14 years with the city so far.
B