no, you do not "need" a corner desk. a boom arm can be attached to generally any desk. in fact, a floor stand is probably even better due to being away from all vibration and would give you even more options for mic placement.
what type of desk you need depends on your individual needs and room layout. for some the angled desk sides may be a convenient location to place a webcam and microphone which would get a nice angled shot. you could get a similar effect on a straight desk if you positioned the boom arm that way and the webcam on a farther corner.
in short: convenient yes, required no.
for instance you could get away with something like
http://rapid-elearning-blog.s3.amazonaws.com/0814/microphone-desk.png
even bigtime gamers...