Assuming that the camera does not shake during long exposure photography, How does the sharpness of the image get affected? Would it be more sharp, less sharp, or remain the same?
In a perfect camera with a perfect sensor, sharpness would remain the same. No such thing exists so you have to consider two possibilities with whichever camera you have. The long exposure causes the sensor to heat and increases image noise:
Your camera does not like that and therefore applies long shutter noise-reduction to clean things up and you get a less sharp image.
Your camera is oblivious to the increase in noise and leaves it there. Speckles caused by noise destroy some fine details but make the image appear sharper sometimes.
A long exposure allows light to accumulate over each imaging sensor for a longer period. This can create a saturated (bright) image which doesn't have anything to do with image sharpness in the technical sense. However, the perceptual effect is that of a less sharp image.
If the distance to the subject is long (10s of meters) you might experience atmospheric distortion which can reduce the sharpness over time. It's not a big problem unless the sun is shining or you have other heat sources between you and the subject.
CCD-type digital image sensors can also exhibit a blooming effect after long exposure times. This is particularly acute in astrophotography, where exposure times of many minutes are normal. The bloom usually radiates out as vertical and horizontal lines. This is more of a problem in a scene with sharp contrasts (e.g. stars against black sky) than it would be in say a terrestrial night scene. Not all sensors are designed with this in mind, since not all manufacturers think of astronomy as a target demographic for their products. EOS Rebel was one that did. Older DSLRs often used CCD, whereas newer DSLRs tend to use CMOS-type sensors that don't suffer from blooming. Many small compact cameras still use CCD.
I guess it depends on what you consider a long exposure. I know on photographer who considers 1/20th a long exposure. Me, I consider 4 seconds, or 15 seconds a long exposure.
I saw a big increase in sharpness when I upgraded my tripod. The old one just wasn't up to the task.