Unfortunately not, amiga native screens are completely unaffected by the mediator/voodoo.
Scandoublers pop up on ebay, you may also want to post a wanted ad here or on
www.amibay.com. Some video cards like the Picasso IV have a built-in scandoubler, the Cybervision 64 has a passthrough so you can route native video (presumably from a scandoubler) to the same monitor. Also, there will eventually be an A4000 version of the Indivision A1200 scandoubler (a fantastic piece of hardware).