In reply to the question in the thread title, yes, applying earlier does improve your chance of getting the College you specify. Departments are required to give equal consideration to all applications submitted up to the 15th January and that can mean hanging on to a lot (not all of them, mind) of applications so that they can make a proper comparison once all the on-time applications have been received. Colleges are not under the equal consideration obligation and have to make decisions promptly so applicants can get a quick answer once their departments have made the decisions about whether the applicants will get offers from the University. The net result of this is that Colleges can fill up in certain subjects early in the cycle if they're popular for those subjects and will then have to pass on any subsequent successful applications in that subject to other Colleges. Thus an early (successful) application will stand a better chance of landing with the preferred College if it's submitted early but there are no guarantees. It does take a long time to reach a decision on some applications, particularly in departments where there are vastly more top drawer applications than the number of offers the department can make. That can mean an application submitted early finds its way to the preferred College after that College is full.
As for the suggestion that a Department might reject early applications because they were judged too good and unlikely to take up the offer, it defies logic. Even if there is individually a small chance of each of these excellent applicants taking up their offer, the dept may get some of them if it makes offers to them so the dept simply takes that into account in the number of offers it makes and end up making more offers. I guess it's just possible that some admissions selectors at some Universities might have done what was described in the past, especially in the days when Universities could see what other Unis applicants had applied to, and that may explain where the information came from but the University would crucify any department doing that today.
...we were on a break