Looking at the code, I think you could replace the code of line 243 of the FileUpload snippet:
243 $uploadfile = $path.basename($_FILES['userfile']['name'][$i]);
with this:
$uploadfile = $path.basename($_FILES['userfile']['name'][$i]);
$profile = $modx->user->getOne('Profile');
if ($profile) {
$profile->set('photo', $uploadfile);
$profile->save();
}
I'm not positive that it would work, but it might be worth a try.
You'll want to duplicate the FileUpload snippet first, make your changes to the duplicate, and use the duplicate on your page.
You'll also want to use this property in the snippet tag so there will only be one input field: