I am trying to find a GIS software that does this, so I am trying QGIS but other suggestions are welcome.
I have a basic shp boundary such as a rectangle. I want to be able to import an unreferenced image (such as a tif or jpg) and place it as a new layer without needing to reference points immediately. I want to be able to use handles or another tool to re-size or stretch it in comparison to my shp. I realize this file is not necessarily referenced in this state even though it is floating over a referenced layer. It does not necessarily have to be saved as a referenced file ever as long as I can see it as an overlay while I work.
Basically because the image I am importing is not actual imagery and does not currently match anything on the map, I want to be able to place it in a way similar to placing and stretching an image in Microsoft Word.
Here's a sample image I photoshoped of what this feature might look like:

Is there a way to do this in QGIS, or suggestions of other software?