|No it wouldn't post if the CPU were bad. The motherboard needs the CPU to do the Power On Self Test to begin with. By the time you hear the POST bleep the CPU has executed a few million instructions.|
However there are many other things that will prevent a computer from posting and a bad CPU is the least likely culprit unless you have done something to damage it like run it without a heat-sink or given it too many volts..
Power supply, memory, and video can all prevent a computer from posting if they are faulty. The fact that the lights are on and the fans are spinning doesn't necessarily mean the power supply is good.