I think some clarity would be helpful in this instance. My SO is attending medical school and went through admissions at the same time i was going through the veterinary school process.
So to clarify, rolling admissions can be used in two forms. One form is with the medical school sense, where the more quickly you get your application in, the faster you get an interview and the faster you get an admission.
Veterinary school admissions is NOT like that.
There is no benefit to applying early. For me, there is only a benefit to waiting, but NOT waiting till the very last second. I say that because what if you have an awesome experience during the summer and want to include it on your VMCAS. If that happens, then you are out of luck if you have submitted your VMCAS.
However taking time and reflecting on your application, asking others to review it, will only strengthen your application. Then you can submit in a relatively good time frame and not have to worry about the system crashing on you. Happened a couple of times last year!!
I know you are all out there stressing, but trust me, getting it in on July 1st does you no good as compared to September 29th. There is no difference!!
However once you have submitted your application, and you get supplementals then the time race is on and really there is nothing you can do about it.
Also to clarify, The Ohio State University, and University of Pennsylvania also have rolling admissions. This is in the "true sense" of the word. There once they offer you an interview you should take the earliest date!!
They admit on a rolling basis until they fill your class. If you get an interview too late then you may be out of luck!
So I just wanted to clarify these differences. For those of you worried about applications, please make sure you have additional references together as some schools require more than one veterinary reference (like THE OSU).
Hope this helps!