Is the iPhone 5s Voice over LTE (VoLTE) capable?
According to all sources I checked the iPhone 5s hardware is capable of VoLTE. 
As you probably know, recently Verizon announce the feature most likely to highlight it during the upcoming iPhone 6 release.

http://9to5mac.com/2014/08/26/verizon-rolling-out-volte-in-coming-weeks-ahead-of-iphone-6-ios-8/