The page does not mention what is the default behavior whenever a function is replaced while the same function is being used in another query/transaction.
Does the query fail? Does the 'CREATE OR REPLACE' operation fail? Does the query finish before the function is replaced?
As a side note, my interest in this came from our need to use 'C-Language Functions', aka binary functions, so it would be neat to also add what is the behavior on those as well, if there's any difference.
IIUC pg_proc is administered using MVCC behavior just like any other table. What you experience will be subject to your isolation mode but in no case will a single command's execution see different versions nor will such execution prevent the "replace"ment of the function with a newer version.
Absent guidance to the contrary I wouldn't expect C language functions to behave any differently than any others. But that just pertains to the "REPLACE" aspect. You need to read the notes about C language functions to get the rest of the story (and you likely wouldn't need to "replace" a C-langauge function entry because of this different loading/compiling mechanism). Namely:
In short, C-language functions, referenced simply by name and module, and pre-compiled, do not have a mechanism to invalidate the cache like pl/pgsql functions do. Other languages may involve yet other dynamics.