Simply put: no, you do not need a mixer to start podcasting. But there are reasons why you should look at getting one:
- Recording with multiple microphones for guests
- Recording a Skype or phone call
- Greater control of sound
- Better sound quality
If your podcast has more than one host, or if you're taking regular calls then a mixing board is recommended. Otherwise, try a few episodes without one and look to get one in the future.