Is it possible to gather DTMF and speech inputs simultaneously?

Yes. GetInput XML supports simultaneous detection of DTMF and speech inputs. Enable this functionality by setting the inputType parameter to "dtmf speech". With that setting, the first input to be detected is forwarded to the Action URL you specify. For example, in response to a prompt like Press 1 or say Yes to accept, if the caller presses 1 before saying anything, then the digit 1 is forwarded to the Action URL.