The trans is similar, so yes - with modifications. Have you still got your 97's old / dead trans? You'll need parts. Your 89 GL probably has 90mm output flanges, which you will need to swap for 100mm to fit your 1997 axles (use the flanges from the 97 trans if you have it.)
You'll also have to use the 89's 8v clutch disk. The input shaft on the 89 trans is smaller - the 97s use the same larger shaft that the 16v units use.
There may also be brackets / mounts / linkage that you'll have to rob from the 97 and put on the 89 (I don't know what all there is - I've never worked on an A3)
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