Looks very similar to how I set up my extraction fan, I also had to add additional ducting to move the air from the tent out of my grow room to combat the heat generated from the HPS light.
fans like that can be pushed or pulled,although if you push at full speed it does take a toll on the fan,I pushed through a carbon filter for a couple of years.
If I use ducting to place it on the floor it will be too far away. What do you think?
Sorry pic is sideways. In bud room I mount vertically up top in corner to pull hot air out. In my overflow quarantine backup area I mount horizontally so I don't have to duck to get in. But they are both up and as far away from intake or mini split as possible
That will work though you may want to support the fan a little. Also I would put a +12" piece of ducting on the outflow side. I don't know why but the work much better that way.