DPA and Job monitoring

Yes, a Database Job Failure alert can be configured. To do that, click on Alerts and go to the Manage Alerts tab. Choose the Administrative option and select the SQL Server Job Failure alert and configure as needed.

Can I limit it down to just the backup jobs I care about?

You can do that by using a custom alert referenced in this Thwack article: Job Failure

In the SQL statement, you can add something like this to the WHERE clause to limit the alert to specific jobs:

AND t2.name IN ('Backups - PROD', 'Backups - DEV')

Note: The #FREQUENCY# is placeholder that DPA substitutes the alert execution frequency value, e.g. if the alert executes every 10 minutes, it will substitute 10 and cause the query to look back 10 minutes for job history.