Customer Effort Score - Is it another way to measure employee engagement

I've recently been doing some reading about Customer Effort Score (CES) and the relationship it appears to have with customer satisfaction (CSAT) and customer loyalty (CL), as measured by Net Promoter Scores (NPS).  If I understand the literature, as customer effort goes up in service engagements, so does the company's "detractor" rating within the NPS metric.  And NPS therefore goes down.  This got me thinking about the theory espoused by Heskett, et. al. in the Service Profit Chain (http://hbr.org/2008/07/putting-the-service-profit-chain-to-work/ar/1) where employee engagement is postulated to be a driver of CSAT.  Though I've always believed that employee engagement directly affects CSAT / CL, I had difficulty finding companies that were mapping employee engagement metrics against CSAT / CL metrics.  So, how could anyone really tell?  It obviously made sense, but how much increase in employee engagement was needed to improve CSAT / CL meaningfully.  And, at what cost?

Anyone who's done customer support work knows that he or she can often place more of the effort of problem resolution on to the customer, if they want to.  Or, they can take more of the effort on to themselves.  Highly engaged employees try to shift effort on to themselves in the full knowledge that the effort avoided by the customer increases that customer's loyalty and satisfaction.  Less engaged employees do the opposite, shifting effort to customers where possible, with the concurrent side effect of lower satisfaction and loyalty over time.

So, in my mind, Customer Effort Scores are a proxy for an employee engagement metric.  One which can be implemented by the support organization itself.  And, if done correctly can track back against the support and account people who are ultimately responsible for the revenue associated with the effected customers. 

CES is the missing link, literally, between employee engagement and customer loyalty.