Marked isn't an editor, it's a parser/previewer utility, so you keep your document open in the editor app (Byword, in your case) AND in Marked. Whenever you save changes to your document in the editor, Marked updates and shows the document all updated and rendered nicely.
Not sure about the wording on that description, may have to email AppStorm to ask for clarification myself.
If you like to type in Byword, but want to preview your rendered Markdown document in Marked, then QC doesn't need to be part of the equation there at all. Just open the document in Byword and in Marked, and type away.