Access custom billing field in rules using Commerce
If you have added the e-mail field on the commerce profile type as you said, you should access is via the profile type as well. (It is not a property of the commerce order.)

Normally, the commerce profiles are already available when the commerce order is loaded. But you might not recognize them as such. Nothing indicates it it a profile.

For instance I have access to these profiles:



And then you can use a condition like this:

  { "entity_has_field" : {
      "entity" : [ "commerce-order:commerce-customer-quotation" ],
      "field" : "commerce_customer_address"
    }
  }