I had a discectomy (L4/L5) with no fusion and had a vaginal birth with DD. (I also have two lower prolapsed discs which haven't been operated on.)
That said, full labour went on for 5 days and no-one could work out why DD couldn't turn or get in position so progress was extremely slow (obviously - it took 5 days!) until they induced me. It was suggested afterwards that the back problems/spinal damage could have been the problem (but no-one could give me any good advice on it pre-birth). DD was very very nearly an emcs (ventouse before fully dilated) but I'm glad I went through with it. (The midwives were great which helped.)
I had an epidural after the induction drip, for which a consultant anaesthatist had to be consulted at 4am, which wasn't fully effective but i was warned about that. (I had to see an anaesthetist earlier in the pg to allow this to go ahead.) I wanted to use a pool, but the induction pain meant this couldn't happen. In the hospitals I was in, the preferred site was L4/L5 which meant they had to do something different in my case.
Obviously, I didn't have a spinal fusion, but I wouldn't immediately see a reason why you couldn't try for a natural birth if you wanted. OTOH I had a CS for my second DC for other reasons and had a spinal (not the partially ineffective epidural) - had that not worked I'd have had to have GA. The consultant did try for a natural birth (another induction), but labour didn't start at all.
TBH I found it impossible to get any decent advice.
Good luck with the birth anyway.