Don't buy a used machine unless you know for certain you can get it serviced before you use it.
When I was faced with the same issue - original recordings on 2 tapes, needing to be copied to computer disk - I went back to the studio where the recordings were made. The engineer had 1 of his 2 original machines still working, so we copied the 8 tracks from tape A all in sync with each other, then 8 tracks from tape B. There was no sync between the 2 tapes (required 2 machines working in sync with each other) but I was able to re-sync them in my DAW.
If your recordings were made as 16 bit, then you can play them back on either a 20 or 16 bit machine. If they're 20 bit, then only a 20 bit machine can read the tape correctly.
I don't think there ever was an 18 bit ADAT machine.