I suspect that you will be able to edit RED Epic but the going will be slow. Several comments:
- reduce your preview window resolution until playback is "smooth"
- you may need to do a sequence / render entire work area if your system is not fast enough to keep up - especialy if you are working with multiple RED layers (multi-cam, etc.)
- hopefully you have at least 8GB or RAM in your laptop, and I suspect more would be better
- definitely use multiple simultaneous drives to share the data transfer load; your laptop has (2) USB 3 ports + I think a eSATA port. If the 3 external drives you have access to are all USB 2.0 find some faster external drives quick! As Chester points out a RAID 0 eSATA solution would work well if you need to buy something.
Good luck and do report back here how it goes!