Obviously PT is important, and not meeting standards can cause problems down the line in your AF career, but not when you first get to COT. I was just at COT last year and I don't think it has changed much since then (from talking to others). The way it worked for us is that the first week we took a PT test and got a score. If you failed that first one, either in any single component or overall, there were consequences at COT - if I remember, you were ineligible to hold leadership positions at COT, ineligible for distinguished graduate, and maybe you stayed one phase below everyone else for privileges until you remediated (I may be wrong about that last one). But that was just at COT, the PT test score itself didn't carry over to your AF file.
Then I think people got chances to remediate during COT, so you can phase up with everyone else. Then, near the end, you take another PT test. It's to see how you've improved, and if you score above a certain level then you get a bullet on your training report. Even then, if you fail any component, you still graduate from COT. I know this because I know a few people who failed both PT tests and still graduated from COT. Basically, the PT tests at COT don't really count. Even people who passed or got excellent scores still had to go to their first duty stations and take a "real" PT test. Now, if you go to your first duty station and keep failing then eventually your career could be in jeopardy but don't worry about it for COT. Just try to get in as best shape as you can before you go.