In AE, I might or might not. It would depend on the sentence and the context.
Here is the definition, from the WordReference dictionary: "any nonhuman animal, especially a large four-footed mammal".
This says the word can used for the animals you mentioned, but most often is used for large four-footed mammals.
The main point of the word "beast" is "non-human". A typical sentence is "Don't assume it has human emotions like shame. It is only a beast". This could be said about a fox, a mole, and most other animals.
But if you said "I was in a forest, and heard the sound of a beast" you mean it sounded like a large mammal like a bear or boar, not an eagle or a fox.
I doubt we can generalize. 'Beast' seems to me to be a literary, dramatic or medieval word, or, a word that's used in a variety of varied but specific contexts, sometimes harmless.
The same goes for its cognates like 'beastly'.
'Monster' might be a more suitable word for a huge and vicious animal.
A vulture is a bird. It does what vultures do but that doesn't include attacking living humans, for instance, so it's not regarded as a malicious threat.
We'd need a specific context to discuss the use of 'beast'.