I have tried the Chinese Schick (yellow) blades to little success in the Supply, although they have been well used in my Schick injector. A slight peculiarity I have noticed is that the Schick key does not work in the Supply at all - despite experimenting with the different settings and loosening the screw, I have to manually load the blade. This issue doesn't appear to be described anywhere online, which again has made me wonder if the razor may be defective.
I find using the schick blades the injector pushes a bit high and unless you guide it down, you end up moving the blade on top of the other one. However, I now manually load the blade like you would with a DE that you would disassemble. Tricky the first time but easy after that. The Supply supplied blades are awful. I didn't know how awful until I compared them to the schick. So that's all I use.