Sort of. You wouldn't do this with Status, you do it with transitions. A status is an indicator of where an issue is in the process, and the assignee is not related to this.
A transition changes status, and can update other fields as well, and that's the correct approach to this requirement. The short answer is "set the assignee in a transition post-function as it moves into a status". So transitions leading to "To Do" would have "set assignee to Eddie", transtitions to "In Review" would have "set assignee to Dan" and so-on.
You'll need a different workflow for each combination of users, which is a bit clunky.
I don't know exactly what post-functions you have available for Cloud/OnDemand but I've used ones from common plugins in the past that are a bit more clever. For example, have user-picker fields for "developer" and "tester" and copy them to assignee in post-functions. Or there's an "assign to last person in developer role who touched this issue". Or there's an "assign to the first person in the developer role". Or "assign to person doing the transition" (handy for support type stuff). And so-on. They're all a bit more flexible because they look at dynamic data.
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