AMD processors are not that low quality, but usually lack processing power when compared to Intel. I think you should be ok with some AMD A8 for example, but haven’t tried it. Also Serato doesn’t support AMD at all so you can’t use just any software.
Bigger problem are low powered processor that both Intel and AMD are selling in supermarkets. Atom based stuff is too weak, same goes with AMD E-series, possibly even laptop versions of A-series at some extent. If you use light software (not Traktor or Serato, DJuced at least), I think you can manage even with low powered processor. I got Haswell based celeron and it’s more than enough powerful for playing with 2 Gb ram. In Windows I think you should have at least 4 Gb.
Some Chromebooks are also ARM based and while it isn’t that much of support problem in linux, ARM still lacks the horse power for desktop use. With tablets the software and OS is wee bit lighter and they can work.
As they say in DDJTips, you have to choose program first. There’s one free called Mixxx (I’m not aware of other proper possibilities with Chromebooks), that works in Linux. Chromebook kernel doesn’t support midi, so you can’t use any controllers with this/Chrubuntu. You need to run other operating system and kernel somehow.
I played my first set with Chromebook hardware yesterday and yes, it is possible, but you basically have to use other operating system. I booted distro called DidJix from usb drive. Worked about correctly, touchpad just needs drivers/you can use mouse.
http://didjix.blogspot.fi/
You can try the distro with any X86 computer and decide after that if you want to start playing with Chromebook/this.