At last company we used an online tool to screen junior/intermediates and the whole point of that tool was "Here's the task, here's the tests that need to pass

At last company we used an online tool to screen junior/intermediates and the whole point of that tool was "Here's the task, here's the tests that need to pass when you're finished, feel free to write more", and someone writing more unit tests to exercise their code was a big positive. Asking someone to implement stuff without running it sounds counterproductive to me. About as effective as asking them to write syntactically valid code on a whiteboard.