You would first need to specify exactly which model of Case and which power supply it would come with, (even though you did mention the 340 watt Enlight). Then some relative judgements can be given as to the probability of that particular PS being usable in an AMD system (which you have yet to specify the CPU type or Speed).
Next, as was mentioned, even if a PS says it is "AMD Approved" doesn't mean it will work on ALL AMD CPU based systems. Higher end AMD CPU's installed in a component ladened system will need much more power than, say a Duron 900 "web surfing" system.
Just how did you conclude that (whatever one) that a particular PS would not work with an AK31 MB?