The MTU requirement of 1600 is only for physical devices in the network underlay.
There should be no devices in the overlay that require an increased of MTU unless you have some specific application requirement for it outside of NSX. 1600 MTU is needed in the switches and routers of the underlay because ESXi VTEPs send vxlan encapsulated traffic between the ESXi hosts.
Symptoms of MTU size being less that 1600 is spontaneous packet drops when applications begin to send larger packets among the different application tiers. Latency is not a symptom of MTU being too small.
If you wish to validate that the MTU size is appropriate for NSX, you can perform vmk pings between ESXi hosts using this documentation:
Also consider this KB: