Yes, ATI does run. (Check my DRI link in my sig)
How well they run depends...
- On your ATI chip/card
- On the version of Xorg (Slackware 10.2 uses 6.8, 11 uses 6.9)
- On the kernel version you are using
- On the driver version from ATI
- What kind of chicken you sacrifice. (KFC seems to be OK)
Alright, the chicken is optional. Pizza works just as well, as long as it has anchovies (Penguins, you know...)
As far as dependencies go, you'll find that, as far as compiling, you'll probably have no problems. As for a program needing something else to run, check the documentation. There is very little handholding in Slackware.
Above all: Read the documentation.