Without replaygain your loud songs have a small dynamic range and your quiet songs have a large dynamic range most of which is below the noise floor. With replaygain your loud songs have the same dynamic range, your quiet songs have the same dynamic range, but a larger proportion of the latter is above the noise floor, meaning you've effectively increased the dynamic range.
Only if they're clipped after raising the level, which is often unavoidable but also often not noticeable for the brief transients that end up getting clipped.
In the end, digital volume leveling can't be lossless. So you don't have to use it. But for mixed playlists, it's very nice.
The argument of whether it would be noticeable is a valid one, but it also weakens the strict dynamic range argument. All you can do is use a limiter, which is a special case of a compressor, which is so named precisely because it limits the dynamic range of a signal.
e: to further, I don't understand why you think that would affect dynamic range. Dynamic range being the difference between the quietest and loudest parts of a song. If the loud bit is 10 times the volume of the quiet bit, and you reduce the volume of the whole song uniformly to 1/10 of its original volume, the loud bit is still 10 times the volume of the quiet bit
You've failed to consider the way that digital audio works. If you have a 16 bit audio file, each sample can take on 2^16 values. If you reduce the volume in software, then each sample of the audio stream can take on fewer than 2^16 values. In the extreme case, you could reduce the volume in software so much that each sample can only take on a tiny number of values, in which case the audio will probably be unrecognizable.
Yes I'm well aware of that but that isn't what dynamic range is referring to in the above. The only thing you affect by reducing the volume in a digital signal is increasing the noise floor, or decreasing the signal-to-noise ratio. 16-bit audio already has a noise floor well below what a human can hear for a recording which has a "normal" volume as you might find on any CD. On top of this, when you use replaygain in your audio player, the digital volume adjustment is applied to a 24bit signal, and Windows (or whatever OS) has a 24bit or 32bit float signal path, and then most or all DACs are 24bit (for example newish Realtek integrated audio). So it really makes no difference to effective SNR either.
