It can work, however ideally want to have the DAC output ratiometric to the PVDD, and then you will have a voltage at the op-amp non-inverting that varies from 0some value up to PVDD.
The current at the output will be (PVDD-Vdac)/2.5, which means it works the opposite way of the original circuit (zero output would be maximum current and no compliance).
This means that to get a significant compliance at the output you will need to limit the Vdac to values relatively close to PVDD, but less than PVDD so you will waste some of the DAC resolution.
You have PVDD = 2.0V. The original circuit deliver 0 to 200mA for 0 to 2.5V Vdac, with a maximum current of less than 278mA with a 4.7 ohm load.
If your DAC output varied from PVDD to PVDD - 0.5V (with a maximum above PVDD- 0.695V) you could get similar output current control.
Let's say your DAC actually provides output from 0 to 5V and you can measure the PVDD (which might vary a bit). You could then output the desired voltage, however you would be using only 0.5V of range vs. 1.25V in the original circuit, so a 10 bit DAC would give you less than 6 bits of resolution vs. 8 bits (4:1). Also there would be errors from the voltage measurement which would affect the zero current point.
TLDR: So you lose quite a bit of accuracy and resolution for the simplification, which only removes some inexpensive parts.