In a polite and non-comittal sort of way

i'd like to revisit the translucent-time idea. If Frodo sensed that time was different there; if Frodo knew that he would "be there" even after he was gone, then did Arwen return to Cerin Amroth in the hopes that Aragorn might still "be there" although he was (genuinely) gone? (in a memory sense, or a spiritual sense, or in a time-translucent sense... or other possibilities perhaps...) Did she go hoping simply to hear an echo?
Was Cerin Amroth hallowed because of Amroth or because of Nenya or because of something else? In other words, once Nenya was gone-- was the timelessnes (or time transparency/ translucency) gone also? If Frodo had returned there, would he have felt the same thing he did during his winter there; or would it have just been another forest with nice trees? Was Arwen's final journey fruitless and disappointing, or were the echoes still there?