I would strongly suggest you keep it in that range. Look at it from a few different angles.
1. Like Hornet said, they want you to be concise, if you can't make your point within that amount of space, than you need to re-evaluate your writing style.
2. This is the military...when the AFA says get up at 4:30, eat at 5:30, class at 8, they don't meant @4:30, 5:30 and 8. Obviously it is not an order since you are not in the military yet, but do you want to come out of the gate and already not follow their guidelines?
3. Many profs will tell you they read to 300, and grade on that. Do you want the board to stop reviewing your essay at 300, if you go to 350 and grade you on the 1st 300 words?
4. Finally, by the time you write all of your essays for your noms, the SA's, ROTC scholarship and your colleges, you will be more than happy to stop at 250
FYI, when DS applied to Notre Dame, they said they will stop reading at the word count limit. Politely told the parents, there just isn't enough time to read 15K essays going over the limit. UMiami admissions said, they actually deduct points from their essays when they go past the count...Belief is you are wasting their time by not following directions. Nobody on this forum sits on the board, thus we can't say they do or not penalize...only you can answer if you are willing to push the limit!
I would talk to your ALO. DS's ALO met with him weekly for the month of July editing and revising his essay with our son. We never helped in the essay in any manner, but I do recall the word count was 298