I’m under the assumption that WordPress will first look through all
the functions in my plugins and if it finds one it won’t default to
the WordPress core version of the function?
No. Not counting any pluggable functions that might be added by a theme or plugin, the only functions that you can overwrite in that way– by simply writing a function of your own having the same name– are the ones in pluggable.php or pluggable-deprecated.php but relying on the latter would be unwise. Try it with any other functions and you will get a fatal PHP error.
If any other function have been changed you are going to have to try to duplicate the functionality of the Core hacks by means of actions and filters and that could be a long hard road.
I should also note that WordPress is no longer adding new pluggable functions to that pluggable.php file.