I'm constantly amazed at how many folks don't realize how dangerous neon signage can be. I worked at a local amusement park who had five! fires on the roof of one building caused by faulty neon installation before they gave up and went to another lighting method.
The HV output of that transformer will merrily arc to any nearby uninsulated surface until the ignition point of that material is reached.
Although the transformer itself is potted in a tar-like compound and could probably survive sitting in water without harm, (and I have seen that before too) I'd bet the connections to both line and secondary aren't that watertight.
