If it's a conscious dragon, then it's definitely meaningful. The dragon will have proof of its own existence, which implies that there is an experiment capable of proving its existence.

No. It is, however, suspicious - what led you to hold such a conveniently untestable belief? What do you think you know, and how do you think you know it?

To be unable to produce an experiential distinction from a belief, is usually a bad sign - but it does not always prove that the belief is meaningless. A great many untestable beliefs are not meaningless; they are meaningful, just almost certainly false: They talk about general concepts already linked to experience, like Suns and chocolate cake, and general frameworks for combining them, like space and time. New instances of the concepts are asserted to be arranged in such a way as to produce no new experiences (chocolate cake suddenly forms in the center of the Sun, then dissolves). But without that specific supporting evidence, the prior probability is likely to come out pretty damn small - at least if the untestable statement is at all exceptional.

Can it be sensed by beings other than humans with which humans might communicate? (Or does that already count as a method, however mediated by these alien beings, of sensing by humans?)

If somebody made this assertion, then I would, as MugaSofer, probably follow up with how this person came to that belief. Somewhere along the way there is likely to be some sensation by that human, whether a past sighting that can't be repeated, communication with (what the believer takes to be) alien beings (space aliens, fairies, angels, etc), or even just a vague feeling that a dragon is there. We might get meaning out of it (and then it is very likely, unless interpreted in a figurative sense, to be very likely false).