At Weathertop Strider says of the Witch-king that ‘more deadly to him' than Frodo's sword 'was the name of Elbereth’ (FR 1.xii.198), but he clearly does not mean the mere mention of her name any more than he means ‘deadly’ to be taken literally. Not only does the invocation of her name not kill the Witch-king, but Strider uses ‘deadly’ again in the very next sentence to describe the effect on Frodo of the Morgul knife, which does not kill its victim. To think that he means literally what he says about Frodo's use of the name Elbereth has absurd consequences. For if all one had to do to drive off the Ringwraiths were to say 'Elbereth', they would not be so fearsome: they would be the Knights Who Say Ni. The 'deadly voices' and the 'harsh and chilling laughter' with which they respond to Frodo's attempt to command them at the Ford of Bruinen proves the name of Elbereth alone cannot harm them.
Elbereth must have aided Frodo when he invoked her at Weathertop, but not when he did so at the Ford (FR 1.xii.212-13). It is impossible to say why this would be, but at the river Frodo's feelings and behavior when faced with the Ringwraiths differ in ways that may be quite significant. In the first place he is moved by hatred of the Riders, and in the second he attempts to command them to leave him and the Ring alone. If, as I think, Frodo is trying to harness the power of the Ring to dominate its dark servants here, it seems little likely that Elbereth would aid someone wielding the Ring any aid. However that may be, it seems entirely unlikely that acting out of hatred would win her support.