Is there a way to make a link to a specific page of a PDF file *on the desktop*? Like, how a lot of application shortcuts let you link a particular shortcut within the application on the shortcut - like how the Dropbox Android application allows you to set shortcuts to particular Dropbox folders on the desktop.

I use ezPDF and I can set individual bookmarks within the application, but I'd also like those to be available on the desktop if at all possible.
Technical answer: Yes.
Practical answer: It's hard.

You'll need:

"Manual intent shortcuts" app to add really custom shortcuts on the desktop ( https://play.google.com/store/apps/details?id=net.cwfk.ig88.intents ).
Plus: Knowledge how to generate a specific intent that does exactly what you want to do (install above app and see what information it wants, you have to know exactly what to do).

PS: I had a look at ezPDF and it seems to allow to launch a specific .pdf file by an intent at a given page, so your problem is solvable, but requires deep knowledge of ezPDF and Android's intent subsystem (intent extra data: path, page).

EDIT: Sample for ezPDF, alas jumping to the page doesn't work, but the correct file is opened

Shortcut Name: test
Action: android.intent.action.VIEW
Category:
URI: file:///sdcard/test.pdf
Component Package: udk.android.reader
Component Class (FQDN): udk.android.reader.PDFReaderActivity
Extra Key: page
Extra Value: 14
[ ] Broadcast  

Regarding how to get those values:  

Use a file browser to open the 'test.pdf' file you want to open by the shortcut later.  

adb logcat -d | grep -i ‘test.pdf’
You should see some line like this:
I/ActivityManager( 123): Starting activity: Intent { act=android.intent.action.VIEW dat=file:///sdcard/test.pdf typ=text/plain cmp=udk.android.reader/.PDFReaderActivity }

Manual launch via adb:
adb shell am start -a android.intent.action.VIEW -n udk.android.reader/.PDFReaderActivity -d file:///mnt/sdcard/Books/Effective.Java_2.Ed_2008.pdf -ef page 2