There are three categories—“meaningful,” “meaningless,” and “tautological” statements—at least in Ayer’s categorization. “Statements which are not testable are meaningless or tautological” would be an example of a tautology: just a definition of terms.
Because if you /could/ test the statement to see if it were true (not absolutely true, but, per Ayer, “probable”), you’d conduct an experiment where you took a sample of statements, tried to come up with tests (ways in which they refer to sense experiences that would serve to verify or disprove them), and then saw which ones were or were not meaningful. But in Ayer’s framework, meaningfulness is defined as referring to sense experiences that would serve to verify or disprove, so it’s circular, thus tautological, which isn’t a term of abuse in Ayer’s categorization the way meaninglessness is. He thinks that philosophers deal in tautologies all the time—constructively! -- and that meaningful statements are more in the domain of science anyway.
I just finished reading Ayer’s “Language, Truth & Logic” last night, and from my understanding of it, I think he’d think that your proposal about the appearance and vanishing of a chocolate cake was a meaningful proposal. He said, for instance, that it would be meaningful and reasonable to posit the appearance of wildflowers on a mountain peak nobody had climbed based on the fact that such wildflowers had been seen on similar mountain peaks nearby, or to propose that there were mountains on the dark side of the moon (before it was possible to empirically verify this). He seemed mostly interested in disqualifying propositions that were /in principle/ unverifiable. Now if you’re asserting that this piece of cake came and went /and/ that it’s not just going to be really difficult to come up with a single sense-impression that this fact would have some bearing on, but that it is /in principle/ impossible to do so, then he’d probably say you’re talking rot.
Your example of a spaceship exiting the range at which you could possibly have any interaction with it is another issue. Ayer deals with the “does this tree continue to be when there’s no one about on the quad” question, and says that (if I remember right) since the logical construction “this tree” is composed of both actual and hypothetical sense experiences, there’s no reason why you have to imagine it vanishing when those sense experiences aren’t immediately occurring. Even given this, though, I’m not sure if Ayer would call your spaceship meaningless or merely improbable, since its hypotheticals would all seem to be logical impossibilities.