You can absolutely send AJAX calls directly from components!
Redux is a tool for making shared state globally available to multiple components, and changed in predictable way. In any case where you don’t find this necessary, don’t do it.
Keeping AJAX calls in action creators is convenient when different components make the same API requests and then change the state in similar ways. It is also convenient if you want to avoid firing off a request when there is already some cached data available, and you want to keep such checks in a single place rather than scattered across the components.
That said Redux is only concerned with how global state is updated, and if you just need to make an AJAX request from some component, you don’t have to write an action creator or a reducer for it unless you find it convenient.
Generally saying Redux (and Flux) is what you might consider refactoring your code to when you have many complicated components; not what you should start every component with. You can use only the parts of it that you need (e.g. just the synchronous stuff), or even avoid it altogether in some cases (e.g. a collapsible panel doesn’t have to store its state in a store). Only use it when you understand the specific benefits it gives you in a particular situation, never “just in case” or because it is popular.
See also my answer to “How do dispatch a Redux action with a timeout?”
To address your specific example, you might want to use Redux for this if you use the benefits Redux gives you: maybe you dispatch an action to update the form optimistically and display the new list right away, and merge it with the fetched list when it is available so that the interaction appears instantaneous. That is the use case for async action creators. If you’re not looking at this kind of UX complexity, I’m not sure Redux is necessary at all.
