"how would they find out"
Before I answer that in a wider aspect to the normal considerations I will mention my own interaction with the PPU on this subject.
When I was questioned why i did not volunteer I asked "what confidentiality processes do you think are in place in the actual charity shop?" I live in a small town were an interview would be done by whoever is in charge that day.There is no confidentially document to sign. By previous shopping visits to the shops you hear the gossip. So why would I risk my new identity being disclosed that would allow a society to punish me further? Please do not suggest "legal" safeguards as they are all after the fact; the damage will of be done."
I show / inform my PPU the facts about my life, my projects, the aspects that support me and others in my life; and yes even strangers. If they wish to place me under surveillance they will see my positive interactions with others, be they strangers or friends. They will see how I "protect myself" from any misinterpretations by anyone. By "facing" the challenges imposed on me, they would see I am not the threat society presumes I am because of their interpretation of my offence.
Fact: I informed them I was going to undertake a volunteer role for an estate agent were I showed prospective property buyers around empty properties, and no declaration was required. I just wanted work activity for my CV at the time. I was informed by my previous PPU officer, he would inform the estate agents as I could break my conditions by being alone with a person under 16. I asked how, and he said the child might be with me alone at the property? When I asked how many under 16 year olds he knows buy property his response in not worthy of writing.
Back to the question on "how would they find out?". Unless you have managed to change your identity and the media have not linked it, a google search is quite a common process by employers now.
Learn from yesterday, live for today, hope is for tomorrow else what is left if you remove a mans hope.