Is there any evidence that the Internet, by cutting across
geographical boundaries, is truly connecting us as one world

No. At least, not yet. People of limited means or limited cultural
capital (cannot read or write, for example), cannot join in. So, it is
one rich world. However, even in this one rich world, there are those
who can do what they want, and those who cannot communicate. Internet
in countries such as China, UAE and Syria is highly limited to things
deemed by the regime as inapproriate. I'd be pleased to develop it
into an answer, if you want me to.

Well, of course the Internet is not the only communications network
"cutting across geographical boundaries". So do radio & TV, the
telephone, international transport systems (especially flight), and
even postal mail. None of those means of communication has succeeded
in "truly connecting us as one world", and unsurprisingly neither has
the Internet. But certainly the Internet has increased the scope, ease
and speed of communications between people living in vastly different
places and cultures; and if we ever achieve anything like a unified
world - and that day currently seems a long way off - no doubt the
Internet will have played a part.

In China very soon 111 million people will be online and from my own
experience I can say that technical barriers to stop information do
not work. But just like Americans or Dutch (I'm Dutch myself) Chinese
feel not inclined to look very much accross the border. So even when
there is technically no restraint, people tend to be rather inward
looking for mainly cultural reasons.

Oh yea -- we are world over united in total harmony in outright hatred
of spammers, phishers and general scam merchants.

Best