Drafts does not have an special integration with Asana.
It should be possible to create actions that interface with Asana using there API from script, if you have specific needs to set multiple values, etc. I have not seen any examples to point you to, but should be possible with HTTP scripting.
Asana also has an interface to email tasks, which should work well with Drafts email actions steps. Would be easy to setup with actions pre-addressed to the right recipients - but is likely limited on the values you can set.
The third option would be to use an web-based automation tool that has Asana integration to bridge the gap – like Zapier or Integromat. Both support web-hooks to trigger actions. There’s an example of calling web-hooks in our Zapier integration guide.