They say a picture is worth a thousand words, so let's look at some pictures, shall we? Here i made 3 renders with identical settings, except that for displacement was used 4K 16bit TIFF, 4K 8bit JPG (highest compression quality) and 3K 16bit PNG textures respectively. 3K 16bit should use about the same amount of RAM, as 4K 8bit. As you can see difference between 4K 16bit and 3K 16 bit is virtually non existant, however 8bit JPG shows significant deterioration and also it renders longer (probably because of noisier displacement). So my advice would be - if you want to save RAM, better decrease your textures resolution, rather than its bit depth. That is true for diplacement and normal maps, other textures should be perfectly fine at 8 bits.
P.S. i included memory metrics in render stamp, in hope to see the RAM consumption difference, but for some reason, the difference was almost non existent, although by my calculations 4K 8bit and 3K16bit should use about 16MB less RAM than 4K 16bit. Max was restarted between each rendering, so conditions should be equal, but for some reason, savings were not there.