Simply judging by the specs you should be fine. What kind of noise do you get? Does it appear in every patch or only in certain combinations? For example, do you have a high noise floor already when patching only Rings to the Audio I/O? Try disconnecting all modules from the bus board/flying bus cable and reconnect one by one, starting with the Audio I/O. At which point does the noise appear?
The A-199 can add a lot of noise to the audio path. Try placing the springs somewhere else, make sure both the springs and the cables aren't too close to other electrical circuits. Try replacing the RCA cable with one that's better shielded.
I don't have the A-106-1 but a lot of MS-20 style filters can be rather noisy (by design).
But of course, the AC adapter might well be the culprit.