I have seen waivers evaluated and approved in less than a week and other never get approved. To answer your question is that it will be resolved as soon as possible but no one can tell you how long it takes as each condition is evaluated independently.
Since USMA actually issues appointments right up to R-Day, you never know. The announced final appointments really aren't final until everyone needed to fill out the class has accepted the appointment. If you have a LOA you are better off than someone without that LOA. People decide to decline because they get their first choice but don't tell the other SA until last minute hedging their cards on something happening to their first choice. I would think that if they are serious about you, and want you to attend (for whatever reason) that they would push a decision on your waiver by April 15th or so because most candidates Plan B requires them to commit to a civilian college (especially with scholarships) NLT May 1 or the incoming year. If USMA wants you, they want to get you appointed before you commit or move on and that means April 15th or thereabouts.
You can browse other threads here and see timelines that range from a week to 9 months for ROTC, the major factor is what they are waiving, one issue, two issues, something chronic in remission or something fixed, something minor or something that could cause major problems. From what I have been told, DOD Inst 6103.03 outlines the disqualifying issues. These are determined by DoD in conjunction with the SA's so that ANYTHING that could possibly be an issue is DQ'd by DoDMERB so the individual services can make their own determinations. And I would think, at this point in the process with maybe up to 40% of any incoming class in waiver status that the easy ones would be getting done quickly.