Yes, it should work. I have a mixed setup as well, but with a selfmade psu.
±15v get regulated to ±12v and + 9v
5v is generated from an additional 9v transformer. Current draw is too high for making the 7805 drop some 10v if you use an lcd backlight and maybe additional slave cores and lots of LEDs.
Might even be good to have a 7805 for each slave core.
Make sure that you don´t connect 9v to 12v! 7809 can be driven from the 12v line with no problem. Current draw should be rather small, but still it´s good practise to use a heatsink.