Can a through-the-wall A/C unit be mounted in a window?

Wow and here after all these years I thought they were the same thing.

Well they are the same, basically. The part that is critical is the external vents can not be blocked by the wall, and that’s where the problem comes in - because of the thickness of the wall. However, going from a wall mount to a window should be no problem at all, other than the mount and making sure to tilt it just enough that the condensate drains outside.

I state this with the understanding that the unit has the normal fully enclosed system except the coils and air vents (I have not seen one that was not enclosed, but wanted to cover all the bases).

It seems to me that it could be supported from the window frame by adding rails (red) across the top and the bottom of the sleeve (blue) that catch on the window frame (green).

side view outdoors on left indoors on right.

I'd go with 1" aluminium angle for the rails and attach them to the sleeve with stainless gutter bolts with locking nuts. I'd have a fiber washer under the bolt heads of the lower ones to prevent leaks.

Follow the advice from @Ed Beal and remember to make sure that none of the louvered spots are being obstructed. There is no difference between a window mount or a "through the wall" installation except that the wall installation is a permanent opening.