Is it possible for glaze to splatter from a piece of ware onto the kiln wall at high temperatures?

Yes. Glaze can bubble and splatter onto the kiln walls and shelves. For this reason, keep ware at least 1” away from element grooves. Periodically check your kiln for glaze contamination. Dig out glaze from kiln walls and the bottom with a putty knife, removing as little firebrick as possible.