I can confirm the early oil cooled 3T GTE's had an oil cooler and the water cooled versions didnt have them.
The later ones have a different oil filter housing that blocks off the original feed line to the oil cooler.
Keeping or adding a cooler is always going to be better, if you do remove the cooler from the early version you need to take the expanding valve from teh oil filter housing as it shuts off the oil supply to the turbo at 80 C and then diverts it to teh cooler. OBviosuly if there is no cooler, there will be no oil going to the turbo = a very short turbo life,