In theory, if you can add the hoover's contents I'd say yes but not too much at once. If you've got a lot just digging it into an open bed might be better or, as someone who's constantly amazed by people's online inventiveness, I'd Google 'uses for cotton waste in the garden'. There's almost certain to be something you wish you'd have thought up☺

Since composting reduces everything to it's most basic elements, cotton, silk, linen & wool would be fine in the compost heap since they are natural fibers. Polyester? nope!

Well my Mum once buried an old wool "flock mattress" in the garden under builders rubble and it did rot down eventually. But in a compost bin, especially a small one, I'd only put it in bits at a time,layered with green stuff so as not to overwhelm material that will rot more quickly. Are you talking about a wormery or an ordinary bin that has worms in? I don't think it would work in a wormery but you can pull it apart and bury it in the garden. Any properly made compost bin standing on soil will get worms in without any help. Cut up the cover first ,and do make sure the filing is actully cotton not polyester.