Most DSLRs have shutter curtains that transit the face of the sensor in approximately 2-4 milliseconds. For any particular camera model, barring a mechanical malfunction, the transit time for each shutter curtain will always be the same, regardless of the exposure time. This is the case with shutter times anywhere from 1/8000 second, where the second curtain is 'chasing' the first curtain across the sensor a small fraction of a millisecond behind it, to Bulb mode, where the offset between when exposure begins and ends on one side of the sensor to the other is still that same 2-4 milliseconds.
For a 1/8000 second exposure, a 4 millisecond offset is roughly 32X the length of the exposure.
For an 8 second exposure, the same 4 millisecond offset is a miniscule 0.0005X of the total exposure time.
How readout is done is inconsequential for still images, since it is performed when no light is reaching the sensor after the shutter curtains are closed.
Reason to ask this question is to understand whether a DSLR camera be suitable for an academic research purpose.
Even top level professional cameras are not what would be considered 'lab grade'. The precision required for creative/historical/documentary photography is relatively low. Anything within one-sixth stop is considered acceptable for a camera with minimum adjustments of 1/3 stop for aperture (Av), exposure time (Tv), and sensitivity (ISO). In terms of exposure time measured in seconds or fractions thereof, one-sixth stop is roughly 12%. So if a camera is set to take a photo using a shutter time of 1/250 second (4ms), anything between 1/285 second (3.52ms) to 1/225 second (4.48ms) is considered acceptable.
The other thing to remember is that the numbers we use in the "standard" shutter speed scale are not the actual target numbers. They're rounded versions of the powers of two that were selected at a time when cameras were even much less precise than they are today. For example, what we call 1/250 second is actually 1/256 second (which means we give or take that allowable 12% time variation from 1/256, rather than from 1/250)! So the allowable window for our named 1/250 shutter time is actually +/- 12% of 1/256 seconds, which figures out to between 1/229 seconds (rounded to the nearest whole denominator) and 1/291 seconds (rounded to the nearest whole denominator). But since we like to round numbers to the nearest "5" in photography, we'll call them 1/230 and 1/290 seconds, respectively.
For more about marked numbers versus target numbers versus actual numbers used and why it doesn't really matter for creative/documentary/historical photography, please see: Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?
My application involves using an extremely short pulse laser to freeze motion(as short a duration as 9ns). So I was worried whether rolling shutter will kick in even at long exposures and make my regular camera unsuitable for the experiment.
Yes, as long as the first curtain is already fully open when the light pulse begins, and the second curtain has not yet begun to close when the light pulse ends, the entire sensor will be illuminated by the entire duration of the light pulse. For still images the sensor is only read out once following the end of the exposure. There is no 'scanning' going on while the shutter is open.
As long as your laser pulse is significantly shorter in duration than the camera's flash sync speed (typically around 1/200-1/250 seconds or 5-4 milliseconds), you might consider using the camera's flash sync capability to trigger the laser. (How to do that would probably need to be a separate question.)
We also have some existing questions about high speed photography using very short pulses of light, rather than short shutter times, to freeze the motion of high speed objects. Among them:
What problems might there be with using a laser as a flash source for high speed photography?
How can I capture the movement of a bullet?
How do I trigger the flash in a way that takes luck out of high-speed photography?
Why doesn't a shutter speed of ¹⁄₂₅₀th freeze motion when a flash of that duration does?