Celtavhc, my personal opinion on the matter is that Frodo would have certainly been captured by the Nazgul (and very swiftly) had it not been for the constant help, and guidance he receives from the rest of the members of the fellowship (and others) throughout the War of the Rings, and I’ll give you a few examples.
First off, Frodo would have most certainly been captured in the Shire by the Nazgul if it weren’t for Gandalf being one step ahead, and getting Frodo to leave the shire when he did. Also, it’s Gandalf’s advice that saves Frodo just outside the Shire when he heeds to the warning to stay off the road, not to mention the fact that Sam stopped him from putting on the ring when the Ringwraiths were near. If Sam hadn’t been there, Frodo would have been caught then for sure. The fact that he was traveling with 3 other Hobbits I think helped him make it safely to Bree. If he had been alone, again I feel he would have been captured. Of course we all know that if it weren’t for Aragorn, the Nazgul would have killed the Hobbits at the Prancing Pony, and the same thing goes at Weathertop. Obviously I could go on all day with many more examples, but again my point is that it was the constant heroics, wisdom, guidance, and vigilance of the rest of the members of the fellowship (as well as others) that kept Frodo from being captured.
"I would have the Ring-bearer bring the crown to me, and let Mithrandir set it upon my head, if he will; for he has been the mover of all that has been accomplished, and this is his victory." Elessar