I don't know how your outlet is wired, and if you've wired the plug to match, but assuming that the plug and outlet match yes, that's what you want. In that setup, white to ground is 120, black to ground is 120, and white to black is 240.
Test this for confirmation with your voltage meter. If you don't get 240 across the white and black as you've drawn, then your plug isn't wired to match your outlet.