Yes. When you book a ride in Roundtrip, you can choose to receive an email, text, or auto voice call notification when a trip has been authorized. You can choose as many staff members as you'd like to receive this notification, and can specify each user's notification preference. The Current Status on the Trip Dashboard will also indicate that the ride has been authorized.
Similarly, you will be notified if an authorization has been denied, or if more information is needed to obtain an authorization. These statuses will also be shown in the Trip Dashboard.