Can 3-phase FOC control be done without current measurement?
You appear to have two questions.


  Can 3-phase FOC control be done without current measurement?


No; The point of field orientated control is to ... control the field in the electrical machine. This relies on knowing what the field is 


  Can a FOC control scheme be done using a rotary encoder to measure the
  position, speed and acceleration directly, or is measuring current
  necessary?


Well, Field orientated control relies on knowing where the rotor is so that correctly phase aligned currents can be synthesised. 

A rotary encoder (resolver, analogue hall effect sensing etc...) can be used to measure the instantaneous position &amp; thus derive speed and acceleration.  The existence of position sensing is to complement current sensing. 

Sensorless control would remove the need for a rotary encoder, although the workable schemes end up using voltage sensing so "sensorless" is a bit misleading.