I’ve been watching Letterman when I can for the past year (Australia
got him on free-to-air only several years ago), and sometimes in his
monologue he talks about this guy who gives him the finger every day
when he goes to the Ed Sullivan Theater.

Is there any evidence that this guy actually exists?

markabe,

Yes, this person does exist.  His name is Chad M. Riden.  He discusses
his obsession with Letterman at this site:

http://www.mangydog.com/chad/020102.shtml

A portion of which says:

"Another major part of my calling was to sit near my new home and give
Dave the middle finger every morning as he comes to work. This, to me,
was the most rewarding part of the job."

He also appeared on Late Show with David Letterman on June 20th and
21st, so if you can track down a copy you can see him for yourself.

Chad also has his own website where you can also peruse more of his
unique humor at http://www.chadmriden.com/

Google search terms used:
letterman finger every day

Good job, and fast.