However, using an AMD GPU you won't have the option for hardware acceleration to speed things up.
And on a screen that small, you'll get frustrated as hell trying to work with the interface. I recommend nothing smaller than 1920 x 1080.
But it will still work without hardware acceleration, correct? Do I really need that?
Yes, it will work.
Do I really need that?
That depends on many things. See this article, and decide for yourself: http://forums.adobe.com/message/3558435#3558435
MPE and CUDA with an nVidia card, will accelerate some processes, but not all.
I also agree with Jim, that you will have a very hard time with that display.
The monitor resolution is BELOW minimum requirements. PR may not install at all and if it does install, you will not be able to see parts of the UI, so you have to work in the blind, guessing at where options are, since they are invisible.