"Appealing" to the ECJ
There are two reasons for going to the ECJ - first because you want a point of EU law clarified, and secondly because you're desperate to slow things down.
An ECJ reference can take years and might be useful for, for an example entirely at random, a US corporation desperate to buy yourself time because you've done nothing about something for years and need time to do nothing for a few more years.
However, as ICANN seems to know, you don't "appeal" to the ECJ, and you don't get to choose if you go there. The ECJ is the court's "phone a friend" option: the court decides whether to refer a case, and should refer only if the need guidance on EU law. If something is obvious or clear, they won't do it. "Demanding" a reference will only work if the court (a ) agrees and (b ) is sympathetic to being lectured about data protection by a US corporation.