Would it be possible to have a transparent textured model created by using photogrammetry in the "background" to use as a reference while making a regular 3D model? What would be the best way to go about it?
You could just move the object behind your actual object, a duplicate to the side and a duplicate to the top or bottom and just use it like a normal picture reference in isometric view. If what you want it to build another object overlapping the reference but not have it getting in the way then you can activate the selection filter on the ouliner: If you turn off the arrow on an object it will no longer be selectable in the viewport and it makes it easier to work around it. You can also play around with the display setting to make the object transparent while you work around it.
Depending on the object you are using it might just be easier to not touch any of these setting and just build stuff around it anyways