Would you test drive a new car before buying it?
I submit all my builds to some moderate testing (like a test drive), writing a document listening to my mp3s and a video encoding task at the same time would provide a very good test for a stock machine, also running a CPU stress test for 15 mins just to check if the temps are in an acceptable range, no more than that.
Extreme test like 8 hours prime or overnight memtest are for heavily OCed machines.
So in short, yes, I'd do 1 MEMTEST pass, 15 mins Prime95 and half an hour of heavy usage, it should't take much time and it will save you a lot of trouble in the mid/long term.