Mortal stowaway on elven ships
 

This is a question that has dangled on in my mind. Say a hobbit or particularly stealthy man sneaks aboard an elven ship heading to Valinor through the Straight Road, and assuming they don't get caught by the elves en route what happens when they reach Valinor?

Would the Valar be immediately aware of their presence? I doubt this because the Valar so far as described aren't omniscient.

Could our intrepid mortal stowaway maybe sneak south and even find a nice cave or tree or something and live in Valinor undetected until death?

Thoughts?

To start, I think it would be extremely difficult, if not impossible, for any unauthorized person to board a ship at Mithlond unobserved.
The Elves living there were probably well aware of whomever was walking about in the area, not to mention the Havens themselves under the vigilance of Círdan.

However, on the rare chance of someone being able to get on board and escape the notice of the mariners all the way to the 'gate' to the West, I would suspect the individual would find the ship going transparent around him, and getting less and less solid until they found themselves alone in the water.

The passage to the West was not controlled by the Elves ultimately, but by the Valar, and they had set rules by which no mortal could circumvent. I can't see just hiding on the ship being enough to get to the Blessed Realm.

And if by some grace or fate they did reach the shores of Aman and the mortal person entered would the Valar be aware of this immediately or would the person have to be discovered?

I think we would have to assume that the Valar would be aware of them.

They may not be omniscient but their powers were vast.

There would probably also be many unclad spirits wandering around watching for the new arrivals who would spot any intruder.

I would think their presence would be known immediately.
Valinor was the home of the Powers, Ilúvatar's governors of Arda. He had changed the world in order to safeguard the Blessed Realm from any incursion by any other then the Elves after the disastrous assault of Ar-Pharazôn from Númenor, so I would think after that the Valar would certainly have the ability to detect anyone who got even within sight of it.

Actually, the Akallabêth, as written in The Silmarillion, has this beautiful passage which I'd nearly forgotten, about a belief among the Númenórean survivors exiled in Middle-earth:

Now, the practical part of me says that if that happened, how would anyone in Middle-earth possibly ever have known? But I still love the imagery. And hopefully that answers your question.

I just find it amusing some particularly sneaky man late in the third age has done the impossible-snuck aboard an elven ship and survived to reach the Blessed Land. They sneak off and are immediately caught by some invisible Maia.

I wonder how the Valar would react to such an action?

It doesn't really answer the question, but the essay 'Aman', published in Morgoth's Ring, discusses the idea that, because of the different way time is perceived in the Blessed Realm, a Man's entire lifespan would seem to take little more than half a year in the West. As a result I can only imagine that, from the point of view of the Valar and the Eldar, a Man's life would be so short that he or she would only need to be watched or looked after for a very short space of time before dying.

As far as I know, that essay is the only extended piece of speculation outside of the main narrative in which Professor Tolkien discusses the idea of Men in Aman. It speculates on Men being given permission to enter Aman by the Valar, but describes this and the consequences as "might-have-beens". It is pointed out from the start of the section on Men that "Eru had forbidden them [the Valar] to admit Men to the Blessed Realm". Allowing Men in was against the Valar's law, but I don't imagine a Man being treated as the invading Númenóreans were. I imagine that they would be looked after, perhaps watched and guarded, admittedly, for the short time which remained to them.

I've often felt that the quote Inzil gave implied that Men who accidentally came to the Blessed Realm would die shortly afterwards (which they would, relatively speaking), but now that I think of it, perhaps "before they died" means "while they were alive", in contrast to most Men who would only see the Mountain as their fëar came to Mandos after death.