No. Deleting a task's files removes its outputs and the input files you uploaded for it, but the task itself stays in your Task History with its ID, parameters and cost, marked No output generated.
Its status doesn't change. A task that showed Completed still shows Completed, now with the crossed-out eye icon (No output generated) instead of its outputs.
The charge stays. If you delete a task's files later, its original charge doesn't change (see Why does my task say "No output generated"?).
Finished or cancelled tasks only. Stop a running task first with the x icon (Kill Task) in Task History. Through the API,
POST /Task/InputOutputDeleterejects running tasks.
If you also want the task records removed, send us a message. Full steps: How do I delete a task's input and output files?