First, it's not a issue of detail or sharpness, but one of signal to noise ratio. Second, instead of asking, why haven't you done the obvious thing and just tried it!?

Let's say you ultimately want a post-processed image with 8 bit per color resolution. In theory, that means any additional bits your camera converts color values to represent extra dynamic range you can use by grabbing only a part of the range and still get 8 bits. For example, if your camera makes 10 bit values, then you have 2 extra bits, so you could use 1/4 of the raw range and still get 8 bits.

However, it's nowhere that simple in practise. Those won't be 10 perfect bits, and the dark to light range usually doesn't extend to the ends of the sensor range. Also, just because numerically there is data there doesn't mean good values have actually been filled in.

There is always some noise in the digitized values. How much depends a lot on the quality of the camera and how well you exposed optimally for what the sensor can do. For example with the hypothetical 10 bit values, you could expose 2 f-stops down from ideal. The brightness values would then range from 0-255 (8 bits) instead of 0-1023 (10 bits). However, for any real camera those values will have significant noise on them. This is not a issue of resolution, but you get a sortof "grainy" looking image due to the noise.

In addition to all the above, rarely do you want the raw values to be mapped linearly to the output image. Any non-linear mapping that results in good 8 bits in the image must necessarily start with more than 8 bit values due to some codes being skipped.

All in all, you should be able to expose 1 f-stop, maybe 2, down from ideal and largely get away with it, but beyond that it depends greatly on the quality of your camera. The only way to really know is to try it and see what you get.

Also, if you're going to "underexpose", it's better to let the camera try and compensate than you doing it after the fact. You do this by setting the ISO value higher. For example, let's say your camera's sensor natively does 200 ISO. Instead of taking a picture at 200 ISO that is underexposed 2 f-stops, it is better to expose properly at 800 ISO. That requires the same f-stop and shutter speed, but with the higher ISO the camera adds gain before digitization, and may do some other processing that you can't do after the fact on the digitized raw values.