Yes, you should definitely normalise audio data before supplying it to a deep learning model. But don't use "peak normalisation" and don't normalize each sample individually: use either (a) mean-and-variance normalisation, or (b) PCEN.
More detail follows...
Firstly, your question refers to "ML model" but it's only deep learning, not machine learning in general, where this matters, because of the gradient descent used in training. Many other algorithms (I'm especially thinking of random forests, and similar) are not affected by normalisation.
The most common approach in audio DL is I think the same as the standard approach in image and other deep learning, which is to use the mean and standard deviation (measured on the training set) to normalise the data. (There's a mathematical justification for this by LeCun et al (1998), ``Efficient backprop''. The main lesson is: it's easy for us to calculate-and-remove the statistical moments in the data, so we should do that and let the training algorithm concentrate on the harder part -- it will thus train faster.)
Extra detail: Note that this "mean and variance" normalisation is typically not a per-sample normalization. Instead, it involves adjusting the values of every sample by fixed scaling and shifting constants so that the mean of the entire dataset is 0 and the standard deviation of the entire dataset is 1. (For instance, if the mean pre-normalisation value across all samples is 0.15, you would subtract 0.15 from every sample regardless of the sample's mean.) This avoids the issue of quiet or empty samples being normalized to have maximal values and becoming loud and noisy
You should not use peak normalisation. (I don't know why Audiomentations implemented it! The documentation refers to exporting audio, not to training.) Clipping is not a concern for us when doing DL, because the processing in deep learning is usually floating-point, and going beyond [-1, 1] is no problem. On the other hand, peak normalisation is likely to make gradient-based learning worse, because it does not help us to control the mean or the standard deviation of the input data--in fact it's likely to do the opposite since the max and min value can vary so aritrarily. For example, the "impulse noise" issue mentioned in your question.
Aside from the standard method, there's also "PCEN" (per-channel energy normalisation), which is designed specifically for audio and takes a different approach. PCEN performs a kind of dynamic gain control (a bit like a "multi-band compressor" audio effect) which is designed to ensure that the energy values within each frequency band are mapped to a range that is "well-behaved" for ML. Lostanlen et al (2018) give a detailed analysis of this issue, arguing for PCEN. I've seen quite a few bioacoustic DL projects using PCEN as the preprocessing (and no other normalisation) and it seems to be a relatively safe low-regret option.
Extra detail: Modern deep learning networks often have normalisation layers embedded inside them (with names such as "BatchNorm", "LayerNorm"). If these are applied at the input layer then they might sometimes be equivalent to pre-normalising your data... but not always, so I do not recommend skipping the normalisation.