I don't think it proves Judaism in the strict sense of the word.

However, the claims that a whole people simultaneously received prophecy and transmitted the knowledge down the generations through their people is certainly much greater than the claims of any other religion.

For example, to believe Christianity, you have to believe one person, Paul, had such a prophetic experience. There was nobody to back up whether what he said was true or not.

Even Jesus' supposed ressurection was not witnessed by a great number of people putting the testimony to its occurence in serious doubt.

But in any case, Christians must believe in national revelation of the Jewish people because it it written explicitly in the bible.

The question is then, why would G-d reveal himself so in such an awesome manner to a whole people, establishing a covenant with them, and then when changing the covenant (as Chrisitianity claims), do it in so much more of a doubtful manner.