Eliminate the "Upload" button in Webforms
First, it's worth to remember that file will be uploaded when you push form's submit button, if user haven't uploaded it yet.
Second, you could use AutoUpload module:

AutoUpload is a user interface (UI) enhancement that initiates automatic upload of files minimizing the number of clicks required by a user.
Currently, users must select files, then press the &quot;Upload&quot; button. We found users often don't realize a button press is necessary and mistakenly think their image is uploaded when it's not.
This module removes the extra button press and hides the &quot;Upload&quot; button via JavaScript for a quicker, automatic file upload. When JavaScript is not enabled, it falls back to the &quot;Upload&quot; button.

I must admit that this module conflicted with my custom modules and themes, but as a code sample it was perfect. It's GPL, so tailoring it to your custom needs is perfectly legal.