This should work so long as the account you run the scheduled task using has correct access to the network share where the bat file is located.
Depending on what the script does, I'd stagger the run times by department. You only need a minute or two of variance to minimize the odds of a staggering hit right at 12. Regarding the commenter above who mentions a login script that high numbers of machines hit, computer logins do not occur at exactly the same moment. Even a few second difference between logins will result in different times for the script getting accessed, so his case, while close, is not exactly the same as yours regarding high levels of simultaneous file access.