[Legate of Amon Lanc]

Well, let me put it this way: Sauron did not know that there's some "spy" in Mordor and he did not seek him. Saruman would have made all the effort to catch the Ringbearer if he knew (and he would have known) that the Ring is near, as I said earlier. The second problem would have been the supplies, they'd still have Bill, but the jouney through Drúwaith Iaur and Andrast is without any possibility to easily buy or get food (like they got from the elves in Lórien). Aragorn and Legolas could surely hunt something, but hunting or gathering food sufficient for nine people, including a warrior from Gondor and four hobbits is a task that cannot be accomplished easily and the possibilities would be to either hunt every day (nonsense, since then the Fellowship almost won't move) or always stop, hunt down ten deers and then go several days without the need to resupply.

Also, crossing the river would create a problem later: the people in the Fellowship even talk about it, I believe at the end of the second book, saying that they are lucky that they can cross the river on boats if they choose to. Down there, they would probably need to cross Osgiliath, which was impossible without the use of military power, and that in turn would of course warn Sauron of something happening (he did the same when he wanted to get the Riders to the western bank).

Not that it is a totally bad idea, but the journey would still be very dangerous due to Saruman and the reasons mentioned above. Also, even if Aragorn gathered the Dead, there will be no one to defend Rohan against Saruman, and no Light from Galadriel, and no Gollum (!). Then Aragorn and Boromir would have probably gone for Minas Tirith, in the best case helping to distract Sauron while the remaining Companions attempt to penetrate Mordor. But even if the Fellowship succeeded and Frodo, guarded by Gandalf would cast the Ring into the Mountain, there will be a really serious problem: a Many-Coloured Lord of Rohan, as Gandalf said to Denethor, he won't see allies arriving from Rohan, but foes. And so the Battle at the Pelennor Fields would have to be made one more time, this time probably with already broken gate and lowered number of men. If they'd even survive the first one without the Rohirrim, that is.