yEd does not support OWL natively.
It is possible to visualiza OWL files in yEd by creating an XSLT transformation that transforms your OWL files into yEd's GraphML dialect and opening the OWL together with said transformation using yEd's XML+XSL file open filter.
It is not possible to write OWL files from yEd. Thus Protege would have to support GraphML import for bidirectional data exchange.