I would have said that was worth checking on, but wegngis has said that the seals are the same, and that the wider surface of the axle stub (where the slinger goes) would fit into it if the axle shaft shoulder wasn't bottoming out first. So unless the slinger was sticking out proud of that surface, I don't believe that removing it would have an effect.
Now if it was the seal that was being hit by the axle instead of the spindle, then even that little bit of glorified sheet metal might be enough to make the difference. But in this case, it doesn't look like it.
What I've always found strange is that the bellows seal won't work. Since it actually fits around that wider slinger surface and compresses very easily for part of it's thickness, it seems like it should not interfere with any function.
But if they say to not use it even without the spindle seal, they've obviously run into something before.
Paul