Not completely true. Yes it lifts also the noise up with it, but then again, this is irrelevant for the usage.

Normalizing is done, to make the peak or RMS level to be up to a certain level. In fact RMS normalizing is a bit of a weird one, since it is a way of limiting (hence probably the link above to compressing). It boosts the power of a track, but you rather would do that with a good compressor or limiter.

Peak normalizing however, is just bringing up the highest peak in the wav file to a certain level. So the if the loudest peak is -3dB, the complete file will get a 3dB boost. That way the tracks' dynamics stay the same. Peak normalizing is quite standard and is used to have your levels peaking up to or almost up to 0 dB which makes mixing more comfortable. A track that was recorded too soft however, will have a lot of noise added as that gets boosted as well. But most tracks will have at least a bit spare room up there since we try to record things without distortion in the digital world, so not peaking and clipping too much. Peak normalizing brings them back to max levels, without ruining dynamics. It makes that you don't end up with your faders all up high in the sky or lowering other tracks too much to be able to hear it in the mix..
So ingeneral: that -12db drumtrack (peak) can use that boost. If after that it becomes too noisy, it has been recorded too soft!

In other words: It will for sure not sound "worse" as stated before, because all you do is boost that what was there to begin with. So if the noisefloor was lifted with it, it is not the normalizing which does bad things to your track, but the recording just was bad... Therefore, trimming the incoming signal up to the loudest possible level (so just a bit under the moment of clipping/distorting) in recordings is an essential and critical issue, you always should do properly!

I'll be back...