I think given the right circumstances it would be possible to sneak into Aman before it was detached from the world. In fact, Eärendil himself did it.
We get our first glimpse of the difficulty of getting to Aman when Eärendil tries to find the Valar and ask them to come to the aid of both Eldar and Edain in Middle-earth.
Eärendil found not Tuor nor Idril, nor came he ever on that journey to the shores of Valinor, defeated by shadows and enchantment, driven by repelling winds, until in longing for Elwing he turned homeward towards the coast of Beleriand.
- "Of the Voyage of Eärendil and the War of Wrath," Chapter 24 The Silmarillion
So here we get our first glimpse of the answer. Eärendil could not find Valinor even with Vingilot the ship built with the aid of Círdan the greatest ship builder in Middle-earth, and an elf.
Of course Eärendil was eventually able to find Valinor but only when he possessed one of the Silmaril.
..but sought back once more to Valinor with Elwing at his side. He stood now most often at the prow of Vingilot, and the Silmaril was bound upon his brow; and ever its light grew greater as they drew into the West. And the wise have said that it was by reason of the power of that holy jewel that they came in time to waters that no vessels save those of the Teleri had known;
- "Of the Voyage of Eärendil and the War of Wrath," Chapter 24 The Silmarillion
However
The reaction of the Valar and Eönwë the herald of Manwë reveals to us that this was entirely unexpected:
'Hail Eärendil, of mariners most renowned, the looked for that cometh at unawares..
So I think we can see here that the coming of Eärendil was unexpected and he had indeed "snuck" into Aman. This is a very specific case though as the only reason he made it to Aman was his possession of one of the Silmarils.
For a more concrete answer though we look at the tale Ælfwine the Anglo-saxon who found the straight road and sailed to Aman from Wales. A rather interesting story which can be found in chapter 6 of the Book Of Lost Tales: part 2.
Ælfwine stumbled upon the straight road and ended up in Aman, with no magic to prohibit him going though. Of course, these does hit a snag as Ælfwine can be translated to ('elf-friend') and as some other users have pointed out, may be a kind of 'free-pass' and Ælfwine was a distant relation of Eärendil.
(I need sources for this but don't have my book with me, so see tolkiengateway )
Ar-Pharazôn even made it to Aman as told in the Akallabêth:
And at last Ar-Pharazôn came even to Aman, the Blessed Realm, and the coasts of Valinor; and still all was silent, and doom hung by a thread. For Ar-Pharazôn wavered at the end, and almost he turned back. His heart misgave him when he looked upon the soundless shores and saw Taniquetil shining, whiter than snow, colder than death, silent, immutable, terrible as the shadow of the light of Ilúvatar. But pride was now his master, and at last he left his ship and strode upon the shore, claiming the land for his own, if none should do battle for it. And a host of the Númenóreans encamped in might about Túna, whence all the Eldar had fled.
now there is the possibility that this was allowed by Manwë or Ilúvatar for the following reason:
And all the fleets of the Númenóreans were drawn down into the abyss, and they were drowned and swallowed up for ever. But Ar-Pharazôn the King and the mortal warriors that had set foot upon the land of Aman were buried under falling hills: there it is said that they lie imprisoned in the Caves of the Forgotten, until the Last Battle and the Day of Doom.
Now this might be a strain to assume as we have little to go on but if it is the case then even Ar-Pharazôn's coming was known to the Valar and he would not have snuck into Aman. And this was an invasion and not a "stealthy" entrance to Aman.
Now, the thing is would it be possible to sneak to Aman on an elven ship? Given your 2 above constraints it is possible, but to be totally honest I think that it would be very improbable.