You could have an ''actual airfield QFE''. But an airfield does not have a QNH, unless the runway is a beach at the high water mark.
Well, in some ways it does. If the airfield elevation differs significantly from sea level, the “airfield QNH” could likewise be significantly different from the sea level pressure.
The QNH given to you by an airfield will result in a pressure altimeter reading the airfield elevation when you are on it. If you use a QNH derived elsewhere and the atmosphere is non-standard, which it is pretty much all of the time, there will be an error on your altimeter, maybe significant and possibly dangerous...