The SSP is a one day interview process. I'd be highly surprised if the medical is involved. That was the most cumbersome portion of the interview, and I would say the least necessary. It delayed me from getting the "go" almost a week because the idiots couldn't hook up an EKG properly. I flatlined. That should have given them a hint that something was wrong with the machine. A trip to a cardiologist to confirm that, yep, absolutely nothing wrong with me later, and I got the go for class...

There will certainly be shrink stuff- the extent of which will be determined. They can pinpoint your personality with rather astounding accuracy.