No, that’s not possible.
There’s no way to pre-populate an Asana form, at all - with or without the Asana API. If you need a form that’s pre-populated, you’d need to do it via a third-party form tool as @lpb says above.
The ability to pre-populate an Asana form is a pretty popular request here in the forum: you can vote for it here: Form Prefill values