There have been several experimental aircraft like that [1] [2], but they are more like augmented helicopters than fixed-wing aircraft with VTOL. Aerodynamically, the arrangement is a biplane, and biplanes are rather inefficient because interference between the flows over the two wings reduces the overall efficiency.
Note that in the case of the Sikorsky S-72, the intent was to stop the rotor in cruise.
Thank you. Looks like what I have in mind is called a Gyrodyne[1] or Heliplane[2]. I would expect it would have almost the same range and speed as an airplane with VTOL capabilities. As you mentioned, the interaction between the two flight surfaces may be too inefficient, but the X3 you linked to broke the unofficial speed record, so there's that.
Note that in the case of the Sikorsky S-72, the intent was to stop the rotor in cruise.
[1] https://en.wikipedia.org/wiki/Eurocopter_X3
[2] http://www.aviastar.org/helicopters_eng/sik_x-wing.php