As someone with autism, I can sometimes get overstimulated and aggressive, to the point where I may pick up something in a fit of rage (Usually a remote or something), then I usually drop it - or wave it around a bit.
However, there is a difference between that and what Shaun did - he had to get a bat (I doubt he has one, so he had to go out and buy one, I bet), then he had to go to Lea's car, then he had to wait for her to get to her car, then he had to have his..... fit of rage. Minimum, that took 10 minutes - assuming there is a sporting goods store right across the street from the hospital, and Shaun went right back to the hospital, found Lea's car in the parking garage (Since I doubt she has an assigned spot - she would probably just be in a general staff parking area), and wait for her to get back. So if he was super lucky, he would have gotten there with the bat a minute before she got there. More likely, it was upwards of an hour - given Shaun's need to use public transit, there and back, etc. etc.