Boards do fill up because it is a limited time frame that they meet. Thus, if they have 2000 on the pile and get through 1850. #1851-2000 will be on the top of the pile to meet the next board.
Now, that being said.HQ AFROTC knows historically how many will be board ready by that date, and in turn have enough officers sent TDY to Maxwell to get through the pool.
I have seen people here get their files submitted a week before and still get boarded.
Just my opinion, but submit the best package, instead of submitting 1st. 1st boards are not necessarily your best option because of how the last few years have worked. Years ago they would do what posters here call re-boarding. If not selected on the 1st, than they would review again and again until the last board. Looking at these board dates it appears they are keep with their new system. If not awarded a scholarship on your 1st shot, you will get 1 of 2 notifications.
1. Sorry, but for FY17 we will not be offering you a scholarship...end of game,
2. At this time we have not made a decision. We will re-board you Mar 27th.
First boards typically are for those that without a doubt will get a scholarship no matter how many submit for the later boards. It is usually a smaller amount than let's say the Jan. Mainly because they also want to see a larger pool size for anyone on the cusp level. Hence, if your SAT or ACT best sitting for Oct. will not be there for the Nov. board, you might want to re-think trying to meet the Nov. board and go for Jan.
~ IOWS if you are still in that 27/28 best sitting ACT, than decide which path you want to go down.
Good luck.