Re: The Library of Congress already has this in hand
In the UK the libraries of deposit are the British Library & the Bodleian in Oxford (not sure if Cambridge also gets a copy). I believe TCD library serves that purpose in Ireland.
The libraries might serve a useful purpose for proving publication but it seems unlikely that ant oher proof would be ignored in court. My local history group has published a number of books with a small print run and we certainly couldn't afford to spare a couple of copies; we're out of print too quickly without that.