As you say in your question, modern logic (really a combination of Boole, Brentano and Frege) treats universal statements of the form, "all A's are B's" as hypothetical. They are understood as something like: for any thing, if it is an A then it is also a B. If we then understand the 'if' to be material implication, then because material implications with a false antecedent are true, the statement "all A's are B's" comes out as trivially true if there are no A's.
In modern logic, statements of the form, "some A's are B's" are understood to mean: there are some things that are both A and B. This is therefore false in the event that there are no A's. Hence, it follows that "all A's are B's" does not entail "some A's are B's" since in the event that there are no A's the former is true and the latter is false.
So, at this point modern logic disagrees with Aristotle's, under which "all A's are B's" entails "some A's are B's". Whether you think one is more plausible than another is irrelevant. They are different logics and have different uses. According to Grice, the fact that "all A's are B's" does appear to imply "some A's are B's" can be explained using the theory of conversational implicature, but that is perhaps a topic for another question.
The usual explanation of the difference between Aristotelian logic and modern logic is that Aristotle's understanding of "all A's are B's" has existential import. In other words, it is false if there are no A's. From a modern point of view, this is unsatisfactory, since sometimes we don't know whether things of a certain kind exist and we wish to reason hypothetically from an assumption that they might. It makes sense to argue that (P1) all unicorns are animals with the body of a horse and a single horn on their forehead, (P2) there are no animals with the body of a horse and a single horn on their forehead, therefore (C) there are no unicorns. But this argument can only be sound if both premises are true, so we need P1 to come out true.
On this understanding of Aristotle, reasoning about non-existent things is simply not possible. Arisotle assumes that we speak only of things that exist, perhaps because he is not interested in making statements about things that don't exist.
However, there is some disagreement among medieval logicians on this point. William of Ockham appears to follow this interpretation, and he detects an asymmetry between the left and right sides of the Aristotelian square of opposition. There is one way to prove "all A's are B's", namely show that all A's are indeed B's, but there are two ways to prove it false, viz, either show that some things that are A are not B, or show that there are no A's. Similarly, there is one way to demonstrate "no A's are B's" is false, namely find an A that is a B, but two ways to prove it true, namely, show that no A is also a B, or show that there are no A's.
Other medieval logicians differed and treated existence as a property. On this understanding, neither "all A's are B's" nor "some A's are B's" has existential import. We would have to make an additional claim, such as "some A's are" or "some A's exist" to assert their existence. On this view, "some dragons breathe fire" might come out true if some hypothetical dragons breathe fire while allowing that some might not, but "some dragons exist" would come out false. "All unicorns are one-horned animals" would come out true on this account, even if there are none.
As to what Aristotle himself would have said, it is hardly possible to say. There are interpreters who go both ways on this issue, but it seems pointless to speculate. So, unfortunately there is no categorical answer to your question.
The significance of the Boole-Brentano-Frege approach is that it treats existence as a quantifier and not as a predicate. There are many advantages of doing this, though if we wish to reason about non-existent objects in modern logic, we can still do so using free logic with an existence predicate.