In any reasonable law, you would prove that your procedures require consent before you start sending the emails. If you have to prove things about a specific user, you are already on unreasonable land.
(But then, I have no idea what places have reasonable rules. I have never seen any with this specific failure for email, but IANAL and I haven't looked much.)
They almost certainly keep a copy of that specific version of the UA. They also very likely keep a log of you agreeing to it. And probably none of those would matter in a court (what you actually say on your site and how reasonable the document is certainly matter a lot more).
Anyway, UA acceptance does not require and does not imply in opt-in to your marketing emails.
Watch out, if you get a HTTP GET request on the approve link, it could be the mail provider scanning for malware, not the user. You may need triple opt in :-)
(But then, I have no idea what places have reasonable rules. I have never seen any with this specific failure for email, but IANAL and I haven't looked much.)