Unfortunately, not much can be done while the main hard drive is encrypted, with regards to disaster recovery/repair. McAfee usually recommends decrypting the drive before doing any kind of repair. We have used a BartPE disc with the EETech plugin successfully to run a chkdsk /R on a machine that would not boot to Windows, and/or to recover data from a machine that would not boot.
Refer to page 7 of the McAfee EETech user guide for instructions for creating/using a BartPE disc. https://kc.mcafee.com/resources/sites/MCAFEE/content/live/PRODUCT_DOCUMENTATION/ 23000/PD23751/en_US/eepc_620_eetech_user_guide_en-us.pdf
As for having a Windows backup on an external drive, encrypted, I'm not sure how that would be possible, since it would be impossible for the Windows Recovery program to read the drive if it is encrypted.