How bad is it for someone with dilated cardiomyopathy to drink energy drinks?

Depends: Energy drinks are designed to be a stimulants which can increase heart counteracting beta blockers which used as a cornerstone treatment in cardiomyopathies. I would advise against.

Uncertain: While there is really no research on this question, the physiology would suggest that you should not drink these. The stimulant effect of caffeine and the other ingredients will generally work against the main treatment mechanisms as described by dr. Koch.