There are two ways of looking at this. If we include internal customer service, where the main issue is a technical solution, then, yes, I have seen engineers who excel at customer service.
If we are talking about external customer service to consumers or to business clients, then engineers don't do as well as professionally-trained customer service representatives. There are two reasons for this. One is simply that they are not trained in listening and communications. So, if you want to use engineers for this type of customer service, give them some customer service training!
The second issue is that most people have a basic personality at work oriented either towards people, data, or things. People oriented towards data and things, and working with precision, tend to go for engineering. They may not naturally have the people skills of someone in customer service.
The best solution I have seen was at Hewlett-Packard many years ago. When a consumer (me) had an unusual problem, they immediately arranged a team call with a CS rep and an engineer working together. My problem was solved, and the engineer was informed, so that manufacturing process could change to eliminate all future occurrences of the problem.