A strong answer
No. In JavaScript, reaching await evaluates an expression and suspends the async function's continuation until the awaited value settles. The current JavaScript stack can return so the host can run other work. When the promise settles, the continuation becomes runnable according to the runtime's job scheduling rules.
The operation itself may progress through operating-system non-blocking I/O, native runtime code, a worker pool, or another mechanism. That depends on the API and platform. await does not identify which mechanism is used, and CPU-heavy JavaScript still occupies the thread that executes it until it yields or is moved to a worker.
In Node.js, the event loop runs JavaScript callbacks and coordinates asynchronous progress. A long callback blocks JavaScript from processing other callbacks even if the machine has spare cores. I would separate waiting for I/O from executing CPU work and instrument the relevant queues before diagnosing a latency problem.
Follow-up direction
Explain where the promise continuation runs and why an event-loop trace must be specific to the host runtime.