The real battle is at the state supreme court, because current state supreme court precedent says abortion is a right under the state constitution. Therefore, the Court of Appeals should uphold the trial judges decision because precedent should bind them like it did the trial court, and this is assuming that the trial judge made his decision based on current precedent and the state constitution because I don't think the decision has been published yet.
The state supreme court would have to overrule its current precedent.
Just by a function of law, they will get an automatic stay on appeal of the lower court's decision. All they have to do is file an appeal for now to get a stay. I'm sure the ACLU will request that the decision remain in effect until the appellate court makes its own decision. Then, in theory, the appellate should uphold the trial court's decision because they are bound by state supreme court precedent to do so. Then, we go to the state supreme court where the ACLU will somehow convince a court that has had 20 years of Republican appointments and electorally retained justices that the Court should uphold its current precedent.