What does this resistor do in this RTD wheatstone bridge?
You are correct in that R5 is there for start-up. R5 gives the bridge and op-amp a symmetrical bias to work with. R6 gives the op-amp a asymmetrical offset, but a tiny one, for stability reasons.

It is implied and necessary that R5 have a value outside the operating range of Q1. It is implied and necessary that R6 be in the meg-ohms, far above the values used in the bridge.

A quote from the application guide:


  The R6 resistor is placed for stability of the anemometer circuit.
  Depending on used operational amplifier, it should be valued from 1.1
  MΩ to 3 MΩ


Once the loop is active and Q1 controls the current, R5 has no effect, at least not above the accuracy levels the design engineer wanted.

This also allows for extreme ranges of RTD1 and RTD2, such that if both were to have a very low resistance, then Q1 might cut off, but R5 and R6 ensure that cannot happen.

The bridge could be more accurate without R5 and R6 injecting tiny offset currents, but at the risk of lock-up if the bridge goes beyond tracking range of the op-amp.