Can a vacuum hose on the engine of an 00 focus cause the transmission to slip?

My 2000 focus has been having problems with the transmission slipping. I had the transmission replaced (not the torque converter) and the problem was still there. I was going to look at it the other day and the battery was bad. When replacing the battery i saw a vacuum hose off. The hose went to a small black box on the firewall. I haven't driven the car much since i put the hose back in but it doesn't seem like it is slipping. Since i put the hose on i have driven about 20 miles with no slips. Is it possible for that vacuum hose to make the transmission slip? If not any idea what that hose is for? Any help is greatly appreciated.