Will a late LOR sink my chances?

[LastGradStanding]

I asked a former teacher for a LOR back in November and he agreed. I applied to several programs before the deadline and all other recommenders had their letters in ahead of time as well. This one professor didn't send my letter off until a week ago and he was the most authoritative recommender. He's well known, is the only recommender in the exact field of study of interest, and I got an A in the class. All of the programs had deadlines from mid-December to mid-January and they last letter wasn't sent until early March. This is a huge setback because the preferred program which is down the street from where I currently live (my house is paid off) already had it's PhD weekend. I was counting on this to give me a boost because because I'm dyslexic and wanted to prove myself. The learning disability has wrought havoc on my GPA despite always doing well on projects and I was even a TA at one point. People get a better impression of me in person. I detailed this in my personal statement. I'm not sure that the program does conditional admissions (other depts in the university do) and I'm pondering whether I should tell them that I'm willing to take a conditional admission. The pessimist in me thinks that this will only draw negative attention to my application. I've already butted heads with the secretary who handles admissions before applying. The website said to ask her for details and I did but she wasn't helpful and seemed annoyed that I had asked questions. It seems like an opportunity for good old fashioned sabotage. Should I ask for special consideration or not?

[Quantum Buckyball]

I am very sorry to hear that this happened to you. To my knowledge, most graduate programs will only review completed applications first.

You might still have a shot for graduate programs with rolling admission though.

[LastGradStanding]

Do you think I should contact them and let them know I'm willing to do a conditional admission? I'm also willing to be indefinitely waitlisted. I only live 20 miles away so I can wait until the first day of class in the fall. I'm unemployed right now so I don't have an opportunity cost for waiting.