Can AppleScript be used to downloading files from a web page?
You have a couple options here, oh the power of a mac!

Option 1:

Use the curl command, documented here.

I would use AppleScript to run the Curl command and any other command you need to run in order to fetch the file you need to analyze, process it to check for the updated file, and then use the curl command again to download the updated file.

If you don't want to use AppleScript, Automator is another option.

Option 2:

Using Applescript, you could have it trigger another script written in perl, php, or the language of your liking, which could be written to do the same fetching, analysis, and fetching of the updated file.  This will provide you the flexibility to write in whatever language you choose based on your comfort level with that language.

An example of writing an AppleScript to trigger another file could be:

do shell script "php ~/Library/Scripts/MyCustomScript.php"


For either option, if you write an AppleScript you can use a program like FastScripts (Also available in the Mac App Store), which adds an icon to the menu bar through which you can easily access your AppleScripts to execute them, but it also provides the added benefit of being able to assign keyboard shortcuts to your AppleScript to trigger them even faster.