No it doesn't. It's all the workings of some very imaginative people. (These guys claim to be the source, but they don't claim it is any more than a coincidence.)
Spelling of OSAMA
Let's start with the spelling of OSAMA when you fold the note:
This can be done with any US bill that has a 0 in its denomination; i.e. the $10, $20, $50 and the $100 bills. Simply use the 0 from the number as an 'O' and add 's', 'am' and 'a' from the phrase "United States Of America".
By the way, with this method, the word USSR can also be shown. This doesn't mean that the whole US economic system was put in place by Lenin. Try it yourself. What other words can you find in the phrase?
The depiction does not resemble the burning Pentagon very accurately. Compare it to other scenes that are equally well represented:
Word Trade Centre
The picture of the burning World Trade Center tower on the back is achieved due to the green monochromatic color of the bill, some advanced origami and a lot of imagination. This effect can be achieved with almost any picture of the north view of the White House not taken during the winter.
Here is an example:
If cut at the following places (the edges of the triangle roof)
Then the cut areas are rotated by 90 degrees and put together:
And finally, cut out the chimneys and you get the white WTC burning with green smoke:
If the picture was monochromatic, then the contrast between the lighter background and the White House itself to the dark green leaves creates the feeling of the black smoke, when in fact it's supposed to be green.
This is essentially the process done with the note by origami. So the conspiracy dates back to whoever planted those trees in such a manner to be just on the edges of the White House.
The same can be done with many pictures of the White House, including:
While that picture of the White House was put on the note in 1998 (3 years before 9/11), the White House looked like this from at least 1913 (the year of the postcard shown, source).
The bill doesn't show the collapse of building 7 of the WTC, the impact at the White House (as was planned by the hijackers of flight 93), or at the field in Pennsylvania.
The evidence here is thin and needs a lot of imagination to be seen. The same coincidence can be seen on almost anything if played with enough. Just look at the examples of the other bills that are given in the site and look at how much imagination is needed to get that result.