Can I override the default Cloud Actions when triggering a code deployment through Cloud API?

Yes, use the cloud_actions parameter with one or more Cloud Action IDs when sending a request to the Deploy code endpoint. You can also use Acquia CLI to do this:

acli api:environments:code-deploy myapp.dev myapp.test --cloud-actions="[ID1, ID2]""

To get a list of all Cloud Actions and their IDs, run:

acli api:environments:cloud-actions-find [myapp.dev]