Suppose I reconfigure my HTTP server to add the following HTTP header into every reply:
or some other presumably funny text.
Can this have any negative effect on the server security?
It depends what the header is.
Assuming it is a made-up,
If you build the header value based on something else - e.g. the user's password - then that obviously would be A Bad Thing™.
As long as you don't disclose info potentially valuable to a would be attacker you are fine.