16 bit digital audio has a theoretical limit of 96 dB of dynamic range. Some hearing aid models with only 16 bit processing do some clever special processing to try to exceed this theoretical limit. But if you pick a hearing aid model that has 24 bit processing or higher, at least this should help.
Although the dynamic range of your impaired hearing is reduced (and that’s what the WDRC Wide Dynamic Range Compression tries to adjust and fit the normal dynamic range into your reduced dynamic range), this is simply the issue of the upper limit of the dynamic range we’re talking about here and it really doesn’t have anything to do with your more limited dynamic range.
So yes, this does make a difference the real world, because if it’s garbage in, it’s garbage out. The higher/wider dynamic range for the input mics will result in more natural, clearer sounds just the way they come into the mics. Even if this sound gets compressed afterward to fit into your more limited range, it remains clear and natural.because that’s what comes in.
On the other hand, if the input mics do not have wide enough dynamic range and/or processing resolution to capture the input sound and has to clip it or severely compress it coming in to fit it into the limited range of the input dynamic, then this sound become garbage/distorted. Once the source of the sound is distorted, no amount of processing can un-distort it. Even if translated/compressed into your more limited dynamic hearing range afterward, it remains distorted, and that’s what you hear.
Regarding whether the feedback manager can really distort the sound or not, it doesn’t hurt to try to turn it off to see if it helps.
But generally, most feedback managers employ 3 principle strategies to reduce feedbacks. 1) It does a phase change. 2) it does a small (10 Hz usually) frequency shift, and 3) it may do a gain reduction in specific resonant frequencies found by the feedback analyzer. The frequency shift in general should be the only effect that may introduce some distortion in the way of some warbling/fluttering when listening to single tone sounds. The phase change and the gain reduction shouldn’t introduce distortion per se.