See this older thread on SX20 with third party microphones:
https://supportforums.cisco.com/discussion/11471976/3rd-party-microphones-cisco-telepresence
Your problem might be because your cable doesn't match the jack - the mic input is a four connector plug, not three, there is a fourth for the microphone control. See page 130 on the SX admin guide
http://www.cisco.com/c/dam/en/us/td/docs/telepresence/endpoint/quick-set-sx20/tc7/administration-guide/sx20-quickset-administrator-guide-tc72.pdf
You should be able to do what you are trying to do.