I found out that the K1 does have GPS. My statements above are incorrect. You can run GPS without a WiFi connection. GPS on the K1 is problematic. It seems that GPS worked fine on Android 3.1.1 which came with the tablet out of the box. After taking the Over The Air (OTA) upgrade to Android 3.2.1 GPS stopped working on some tablets. There is a very long thread about the GPS problem on the Lenovo forum:
I read the complete thread. They give you some things to try to get it working. There is one person in the thread who works with Lenovo engineering reporting problems. Hopefully Lenovo will get the GPS problem resolved. They are taking their sweet time.
My pc blew up and I am in the process of building a new one. After getting it built I will play around with GPS and report back on what I find. If you have GPS on your K1 and it is working you are lucky.