No. All colours in the sRGB gamut can be displayed in 8bits. So the conversion from 16bit to 8bit would not give any noticeable difference.
If you open an 8bit image you have limited data to work with. So you bump up the contrast and photoshop starts to make educated guesses. The more you work the image the nastier these guesses get. The first places these guesses become obvious is in shadows and gradients.
If you start with a 12bit RAW from your camera, open it in CameraRAW as a 16bit file, then you have a lot more information to begin with. To put this in perspective: A 12bit file represents 4096 possible values. An 8bit file only 256. So you get a factor 16 increase in data that makes your educated guesses more accurate.