IIUC, literally using @_eagerMove on a non-copyable type was explicitly banned (here), so simply adding the annotation is not possible. You can still place it on variable bindings of such types, but, at least in my basic experiments, it doesn't appear to have the effect of making their lifetimes non-lexical.
From source inspection, it looks like even if the annotations could be applied, they are currently overridden for non-copyable types, which seem to be unconditionally lowered to SIL with lexical lifetimes.
@Andrew_Trick covered some of the possible lifetime "categories" in this related post. It seems like you're asking if it's possible to get the "optimized lifetime" behavior for non-copyable types. Per that post, I would think it may be possible if you had an ~Escapable value that was also ~Copyable but without a custom deinit, but I've not been able to find any examples that actually demonstrate that is the case.