I mean it's easy enough to try for yourself if you do not believe my own experience.
This is different from the Linux situation, in which a file's name and directory location are separate from its inode, or the data structure holding actual information about the file including where the data lives on disk: once the inode associated with a file name is looked up and the file opened, anything may be done with the file name, including changing or unlinking it. Inodes with no links will also only be freed once every open file descriptor on the unlinked inode is closed. So a process will keep on chugging even if its executable file on disk is deleted, as though nothing happened -- because the file itself is only deleted once its inode is closed and unlinked.
Like you it used to drive me crazy and would often doesn't work but I never had issues after doing this.