Oh, it's possible. But it can be a lot of work.
You need to do some digging. To start with I suggest you write your script to use MSXML's XMLHTTPRequest object. If your customers have IE 5.0 or later installed their machines already have this component.
The documentation you'll see on using this component from script tends to be a bit meager though. Most script uses are for GETs or for POSTs of a blob of XML data.
To do an HTTP POST conforming to standards of an HTML form's submit action can be fiddly. More so if you are trying to act like a HTML form with an <INPUT type=file> element in it.
One place to start may be
IXMLHTTPRequest Members but be warned you will not find a cookbook there. The material is strongly C++ oriented, but with a few JScript and VB sample fragments in it.
There is a good reason you will not see much on this topic on the web. The various renditions of XMLHTTPRequest (there are many copies of the IE component out there now, Mozilla has one, FireFox, etc. all slightly different but more or less the same thing) are most commonly used today to implement a thing people now like to call "Ajax."
It's a rehash of a Microsoft technology called Remote Scripting, but what's important to us here is Ajax is done within the context of a web page. The security model of today's browsers does not permit script in a web page to open local files willy-nilly.
Since script can't open local disk files, and script uses XMLHTTPRequest to GET/POST data to a web server, and to POST a file's contents you have to be able to read it... they don't.
The good news is your WSH script will not have such limitations. Um, you ARE talking about a WSH script right? Not script in a web page?
The bad news is since most XMLHTTPRequest users can't use POST with files (as I just described) there is a dearth of samples and advice out there.