No, this is not acceptable. Do not do this. This is not a valid deployment mechanism. This should have been yours or his first clue:
It sometimes throws an exception that the file is in use on his program but if he tries renaming it in a loop it will eventually succeed.
And it won't work, anyway. His theory is quite wrong:
Using that knowledge he wants to rename a running exe and copy over a new version of said exe such that anyone running their in memory copy of foo.exe are fine and anybody who opens a shortcut pointing to foo.exe will get a new copy with updates applied.
Specifically, the copy in memory will not be automatically replaced with the new executable just because it has the same name. The reason that you're allowed to rename the executable in the first place is because the operating system is not using the file name to find the application. The original executable will still be loaded, and it will remain loaded until you explicitly unload it and load the new, modified executable.
Notice how even modern web browsers like Chrome and Firefox with their super fancy automatic, in the background, no one ever notices that they exist, updaters still have to close and relaunch the application in order to apply the updates.
Don't worry about shooting the messenger here. It's more likely that your customers and your tech support department will shoot you first.