I'm not so sure. In recent issues as contentious as this we've had District Courts make Nation-wide injunctions against these EOs, and they've been fast-tracked to SCOTUS. It might take a year or so, but I think "years" is overstating how fast something that's this emotional can get to the High Court.
There's other problems with the "Nation-wide injunction" but if this EO gets issued that'll for sure be the next thing that happens, and I'm sure Twitter et al are counting on it.
