Yes, the batter is out of luck on that.
Some umpires, though it's rare, cover in their pre-game that if this situation arises, and the BU (base umpire, used more often than FU) is going to call it a swing, the BU can go ahead and make that call ("Yes he did!") without the appeal, so the runner has a chance.
This would typically be done at the levels where the PU HAS to appeal if asked by the catcher or coach. I believe in NCAA they have to, in NFHS it's an option.
As a coach, you wouldn't want your guys to just take off on any check swings that get by the catcher. The problem is the defense will NOT appeal if the catcher has no shot.
If I were the batter, I guess I might try running down first pointing at the base umpire hoping he signals something