I very much doubt that he could catch a disease from the other horse. Diseases that spread between horse are fairly unusual, and also severe, so you'd know already if the other horse had a problem. It would be very apparent if this horse was sick. Furthermore, these diseases are either very contagious (such as contagious anemia, the reason for a coggin's test),or not spread directly among horses at all, such as West Nile which is carried by mosquito bites. So, if a disease was contagious they'd all have it, and if it isn't you have nothing to worry about that. On top of that you'd already know if the other horse was sick.
One possible thing to worry a bout would be a colic or founder from eating a lot of other horses' grain. Too much grain can cause a stomach upset, or cause founder, a problem with the lining of the hooves. How many stalls did he get in? Just keep a close eye on him.
Finally, I really don't advise ever leaving a horse tied unattended. They can escape, as your horse did. They can also panic and hurt themselves. If you go somewhere, make sure that your horse is safely in his stall first, unless it's to go get something and come directly back. Even then it's best if the horse can stay in your sight. I always try to get all of my stuff out before I tie the horse up to begin with.
Sounds like your horse will be just fine. Just be careful with him. A few weeks ago I learned all to clearly how fragile horses are and how quickly things can happen with no warning at all. My mare became tangled in a fence, broke her leg and had to be euthanized. These kinds of accidents are inherent to keeping horses, and some, such as this one, cannot be avoided. But, take every precaution you can to prevent these things. Mattie was the kind of horse that could teach you something new every day if you listened carefully enough, which I often didn't. Her last lesson to me was to remember how important safety is, and to make me realize that I was taking my horses for granted. Since then I've paid much more attention to my remaining horse, and have also been a little more conscious of safety. Bad things happen sometimes and it can't be avoided, but you can prevent a lot of accidents with just a little extra caution. Just don't learn the hard way.