The student license is considered "noncommercial". You can read the license terms at https://software.intel.com/en-us/license/eula-for-intel-software-development-products My reading suggests that there's no problem using the student license for research and there's no effect on your ability to publish papers where you used the Intel compiler for the underlying research. The only exception would be that if you are paid for developing the software.
All that said, I don't speak for Intel (anymore.)
