I can't imagine any advantage to try and do anything at immigration before leaving. If he's worried they wont let him leave then equally they wont want to transfer anything. If it's only the chip that is damaged (front cover or back, can't recall) but the photo page (that is the thing that is "machine readable") is intact then I don't see a problem leaving, and certainly not arriving in the UK. If he's intending to go elsewhere then a new passport might be a good idea, but even then the application process for a damaged passport is not necessarily the same as for a well kept one.