On their own, there's usually no timeout condition for async functions like this. The task (I don't know what they're called in gdscript, I use c#) will just hang until it completes, errors, or is canceled.
There are cases when you can run into timeouts, such as sending web requests. There are also use cases for making your own timeout trigger. In both of these cases, the timeout is because of what made the task, not something inherent in tasks.
Thanks for the explanation! Your explanation led me down a rabbit hole of seeing if there's a way to cancel an await call, from what I can tell there was no clear way to do so. In my case I ended up connecting the signal to a secondary function instead of utilizing the await command, I'm not entirely sure if there's an advantage to utilizing one method over the other.