Is there any preference given based on how far in advance of the deadline a graduate application is submitted? During graduate studies online application submission period, is there any preference given for an applicant if he/she submits his application at the beginning of that period compared with someone who submits his/her application couple of hours before the deadline?

Or as long as the applications are complete there is absolutely no difference!
Look at all the application rules and guidelines. Unless the registration/application is specifically described as first-come first-served (which would be unusual), the date of submission doesn't matter as long as the submission is complete before the deadline.