The rough time line is- a long time
Sprint is struggling to fill the many holes in their LTE coverage, get rid of WiMax, repurpose the Nextel network and integrate Clearwire. They are losing the coverage war so this is what they are focused on.
VoLTE requires a whole new internal infrastructure and is definitely on the back burner.
As of now, Verizon is the only one rolling out VoLTE