I have disabled windows update on all of my windows server. Will that cause problems?
It's good practice to disable automatic updates on servers: you don't want them to apply updates and reboot whenever they feel like doing it, and also it's better to not immediately install any update on all your servers as soon as it comes out, without doing at least some testing before.
However, you definitely should keep your servers up to date; exactly how, when and what updates will be applied is up to you (or your company/department) to define, but you really should have an update policy (even as simple as "wait for a week after updates are released, then run a manual Windows Update on each machine during off-peak hours") and follow it.
No, it is not safe.
Having Windows Update disabled means you are not receiving latest security and other updates from Microsoft. Unless you keep downloading and installing the patches on monthly basis manually, this leaves your servers (as well as your whole environment) vulnerable to security attacks. In a long run, this might result in stability issues or data loss/leak.