the 4AGE was in RWD format in the AE86 (85-87) the AE92 coupes (88-92) had the 4AGE in FWD format. I'm not sure where you're getting your info from.. but obviously you're not looking deep enough.
To top it all off.. the AE101 and AE111's in japan had the newer generation of FWD 4AGE's which was 20V instead of 16V per cylinder, Silvertop 4AGE for the AE101 and the blacktop 4AGE for the AE111.
Even better, the 4AGE and 4AGZE ALSO came in MR format in the 85-89 MR2.
I suggest you look at the Corolla master sticky which is the first post in the corolla forum.
To answer your question (without knowing what car you drive) yes you could drop a 4AGE from any car made after 1988 into your car... either way its still gonna be a lot of work due to suspension, transsmission, engine mount differences and ECU harness and wiring differences.