There are some concepts in there you are confusing I believe, this may get somewhat technical however and hopefully I won’t type out an entire book in itself…
Normalization in an ideal digital audio system is only applying gain. That means you are mathematically increasing every value in a 16,24,32, etc. bit signal by a set amount. Talking in floating point systems your range of values will typically be between 1.0 and -1.0. If your audio signal peaks at .5 and -.5, and you are normalizing it, you are taking the entire signal and increasing all of it by an identical amount so that the point in time that did reach .5 or -.5 before now reach 1.0 and -1.0 (Simplifying it slightly). The added effect this has is that you are increasing the quietest parts of the signal, which assuming you are talking about real world recordings(And even if you aren’t in many cases) will NOT be equal to 0, but instead minutely above or below zero. In increasing the level of the entire signal, you are also going to increase that minute level, otherwise known as the noise floor, to compensate.
In a 16 Bit signal, that noise floor by default can only be so quiet, so normalizing would create a very noticeable increase in the signal. This is why when recording at 16 bit you need to make sure you are recording with levels just below peak. In a 24 Bit signal, it is possible for that quiet value to be much better defined and much quieter, so normalizing the signal does not increase the noise floor in as noticeable way, thus allowing for people to get more usable signal out of a signal that was recorded with more headroom. I really don’t want to dwell on this topic quite as much as I probably should as it is a conversation in itself.
So when people say normalization adds to the noise, they are technically correct in that it will increase the noise floor. However the actual amount of signal compared to noise will not change, and in actuality because of this, there is no additional noise or distortion introduced in the process.
Now all this aside…
When dealing with algorithmically generating or modifying sound, you can end up with values that cannot be recorded precisely in a fixed bit depth. For instance multiply .12 by 1.2 and you will end up with .144, which actually needs more precision than either of those values. This tends to be the largest issue when dealing with actual processing more advanced than a simple multiplication, aka reverb DSP etc. You can always increase the bit depth of the saved value, and in fact many systems use a much larger data path internally than the source might traditionally need, Ardour included(Digital Audio only gets recorded at about 20 bits by the best AD converters to my knowledge, Ardour IIRC uses a 32 Bit data path in its mix engine, Harrison I believe uses 64 Bit data paths in its large format consoles). This allows for a tremendous amount of precision for the results to grow into. However you can still lose a slight(Literally, inaudible) amount of audio depending on the processing. So yes in those cases you will suffer a slight degredation of the signal IF YOU ARE DEALING WITH A DESTRUCTIVE PROCESS THAT DOES NOT ACCOUNT FOR THIS BY PROVIDING AN INCREASED BIT DEPTH TO ACCOUNT FOR THE ADDITIONAL NEEDED PRECISION. Otherwise you will always have the source signal that will be unaffected.
Ok all this said, lets look at Ardour and why this really isn’t an issue in a properly designed and implemented non-destructive workflow. When dealing with Ardour’s normalization, what you get is the audio file analyzed and the value needed to actually normalize the audio file is stored in the region description in the session file. For instance one value from a normalized region I have right now is 1.8104865551. This value is then combined with the value for gain presented by the fader itself, region gain, and any other value in that method, to come up with the total gain applied to a region at any given point in time, a single gain operation is applied to the value, not multiple. Thus normalization, even in the extremely minute cases mentioned above, does not actually affect the audio at all by itself, but instead is combined with other methods of affecting gain before the audio data is modified at all.
So… how much of that makes sense?
Seablade