Would you warn them that V'ger was going to take Ilia?
Short answer, no.
First, 21st century me wouldn't have any ID, would I be imprisoned as a stowaway? Do I show up in my pocket T and sweats or am I in uniform. They don't have fat people in the future apparently, would they mistake me for a Tellerite? (I don't have the snout or hooves, but I have shape and hair of one, maybe a half Human/Tellerite) Maybe I'm wearing that silver/plastic square combo jumpsuit they wore.
If I'm not arrested, I'd be interested to see if my savings account has survived and my $25 is now several billion. I'd be interested in either buying an island with naked women or starting my own publishing company so I can write The Hitchhiker's Guide to the Galaxy. I would also need to buy/obtain a towel.
If I got here without the aid of a blue box, then I'd have to accept that everyone I knew was dead, and I might have to go see if I could find my family's graves, maybe with the help of my ambuquad.
If it's like Galaxy Quest, and stuff really works just like it does on TV, then I might actually be able to join Starfleet, but I doubt I'd make it through officer training and have to be a crewman or a cook.
I like the idea of the thread, but it's poorly worded. But no reason to be bothered about it.