SLC may not be your best choice for this. It's good stuff, though. If the old tub was set in mortar, you'll probably need to take it out. Is the floor on a slab or is it wood? If wood, it will probably come right out. If it is on a slab, it probably didn't bond well, and you can get it out as well. SOmewhat depends on what they use, if anything.
SOme tubs come with a foam base that accounts for the slope. If your new tub has this, then the slc may be viable. When I used it in my bathroom, I put some 2x4's across the doorways, tonailed into the frame. Then, I took some duct tape and put it on the floor with a fold up on the 2x4.
If the tub does not have a captive flat base, then I'd set it in mortar. This will support the bottom well, and provide a means to level it and get it at the desired overall height.
The tub probably won't stick to the mortar, but if you are worried, you could place a layer of plastic down before you set the tub in it. If it is a wood subfloor, you want to install either some plastic or felt on the floor to prevent the wood from sucking the moisture out of the mortar so it can cure properly.