Answering for myself: No.
First of all, the U.N. has been severely compromised by the nations, ideologies, and groups in this world that are making most of the trouble in the first place. As just one example, the Human Rights Council routinely includes members like Cuba, China, Libya, and other totalitarian nations. I call that "unclear on the concept."
Second, the U.N. record of actual military peacekeeping is abysmal. For decades there has been no significant difference in deploying U.N. troops to a troubled area of the world than there would have been if they had deployed cardboard cutouts of armed troops.
I suspect it would be no different with a U.N. Navy.
That, and the U.S. would be paying for it all anyway.