She might, but I doubt she will, because then she would be shown to oppose relief twice; once when she refused to make a deal with the Republicans and again when she files suit to block President Trump’s attempt to deal with it.
There is also the spectacle of suing an “illusion.” If none of the EO’s has substantive effect, then why oppose them? That said, I think the DEMs will sue, and be joined by some on the GOP side, like Sasse.