I'm trying to estimate the direction of arrival of sound using a microphone array. This requires me to find the delay of the sound signal upon arriving the different microphones. For convenience, I was hoping to use 4 USB mini microphones and connect them all to a USB hub to create a 4 mic array. Is this possible?
No, this is not possible. The main problem is that the audio sample clocks between the four microphones will not be phase-aligned and possibly not match in frequency. Because of this you won't know how to align the four data streams to do proper processing.
It would be better to get a single 4-channel audio USB interface. At least then you'll know that they are all time aligned and sync'd. You can find many of these types of devices at Sweetwater Sound and Guitar Center.