I have not used the "copy to clipboard" feature for long time so I am not going to comment on it.
However, there is an easier way.
If a valid image file link is displayed in the Image File field you can use the "Update Tags (from library)" tool for embedding the image in the file tag. Naturally you must have the "Also store image in the file's tag" setting enabled in Options > File Location > Cover Art.
Embedding is supported with most, but not all audio file types. MC cannot add cover art to externally decoded files.
In order to make the task even easier you can create a smartlist that shows all files that don't have an embedded image yet. Create a new smartlist with the rule [Media Type]=[Audio] -[Image File]=[Inside File] (you can simply press the "Import / Export" button in the Edit Smartlist window and paste the rule in there). After you have the list available you can also add the Image File column to it and see the field values.