The number of studies available on the subject seems to indicate that the answer should be yes, to some extent. "Microwave data" is a pretty broad category however, including a wide variety of sensors, either passive or active, with each their strengths and weaknesses. For instance some studies using AMSR-E and SAR data have been published. A brief but good perspective on the problem can found in

Paul, F., Bolch, T., Kaab, A., Nagler, T., Shepherd, A., & Strozzi, T. (2012, July). Satellite-based glacier monitoring in the ESA project Glaciers_cci. In Geoscience and Remote Sensing Symposium (IGARSS), 2012 IEEE International (pp. 3222-3225).

thanks, I have discussed this with T Bolch....