I also saw your similar post at the GE Fanuc site. I haven't personally hooked any 4-wire transmitters to GE Fanuc analog input cards, but in over ten years of providing technical support for that product line, I've never heard anyone complain of an inability to do so.
The answer is: "IT DEPENDS". I've used self powerd 4-20 ma transmitters on the 90-30 no problem. Usuallly a self powered transmitter will work fine with any AI card. Howerver, GE has a lot of different models out there, so you should look at the model specific wiring diagrams and specs.