While I suppose it is technically possible to remove all references to this file from the pages you are using I am not sure that would be the best solution. There are actually 2 different core.js files and both seem to have function calls that would be used by everyone.
I am not sure if customizing this file is supported but my guess would be no. Besides there is no guarantee that a hotfix or service pack would not overwrite your changes.
Finally, changing this file would cause the change to occur on all the web applications since they all read from the "12" folder.
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