This should be doable by breaking up the SlickUpload control into its component parts. The SlickUpload control actually composes four other controls: the FileSelector, FileList, UploadConnector, and UploadProgressDisplay controls.
You should be able to put the FileSelector, FileList, and UploadConnector portions on your page, and then put the UploadProgressDisplay control on your popup. Handle the OnClientUploadSessionStarted event to show the popup when the upload starts, and the OnClientBeforeSessionEnd to hide the popup when the upload is complete.
Take a look at the Multiple sample for an example of how to set this up. You won't need the multiple FileSelector/FileList combos that it demonstrates, just the separate FileSelector, FileList, UploadConnector, and UploadProgressDisplay controls.