If on the other server they use require() to load your file then your code will be executed on the remote server. However if they use file_get_contents() or something simillar then your code will be executed on your server and the output will be available to the remote server. Using require() on a remote file requires the fopen_wrappers directive to be set.
A quick check of the manual shows that the directive is allow_url_fopen.
In answer to your question - if they include() or require() your file yes any functions, classes and variables defined there will be available to the remote server.