Research is primarily to learn and discover new facets to any branch/science etc. It is not your normal day to day job that you earn. CSE will take in students from EEE but I am not sure that research in EEE can really be managed by a CSE student. This will depend upon the area of research, institute where it is being pursued and their eligibility etc. Let me know which institute you are interested and may be I can give more details.