I have a little experience with this since my son received a LOA and had 2 medical DQs. He went through the waiver process and was granted waivers on both. He graduated from WP and has been an officer for a few years. IOW - it all worked out!
Some insight into the process -
If you receive a DQ - with a LOA in hand, your RC will request a waiver. Your medical files go to the docs at WP who review your medical information. If they want more information, they will contact DoDMERB and DoDMERB will contact you. You supply DoDMERB with the information and DoDMERB sends it to West Point.
Once the docs have all the information they want, they will recommend to the Admissions Committee to either grant the waiver or deny it. 'Recommend' is the key word - they can only recommend, not actually grant or deny. The admissions committee does that. So technically, if the docs recommend to deny a waiver, it is just a recommendation and the admissions committee can choose to grant the waiver anyway. I'm pretty sure this is rare, but it is within the scope of what the Admissions committee can do.
The Admissions committee has no influence over the docs. The docs do not know if you are a 'walk on water' candidate or not. The docs make their decision based solely on the medical facts. Their objective is to determine if you can be worldwide deployable with no issues with the condition that you are DQ'd for. When DoDMERB issues a DQ, they have determined that you do not meet these requirements. When WP requests a waiver, they are saying that they are willing to take on the risk of your condition.
I know this is not one of your conditions, but just as an example - asthma is a common DQ. It can be frustrating to the candidate who may say that they've been prescribed an inhaler, but they never use it and can run miles with no breathing problems. However, your hometown most likely does not mimic the same conditions that are in Afghanistan with its dust and sand. You can not afford to have an asthma attack in a remote location. It could be not only dangerous for you, but for your troops.
Hopefully, you will not receive any DQs, but if you do, be prepared that it could take a while to hear whether your waiver was granted or denied. In my son's case, he was DQ'd in Sept and received both waivers at the end of April the next year. He still went on his overnight visit, not knowing if he would be allowed to attend WP.
Having a LOA has no influence over the docs. Where it may come in handy is if the docs recommend to deny the waiver and WP decides to grant it anyway. I have no statistics on how often that happens, but I tend to think it is rare.
Good luck and hopefully you won't have to run the gauntlet of the medical DQ/waiver process.