Adding new databases to existing maintenance backup plan
Yes, you can use the well used ola hallengren.scripts.

Make use of the SQL Server Backup scripts available on the above.

Eg:


  Back up all user databases, using checksums and compression; verify
  the backup; and delete old backup files


EXECUTE dbo.DatabaseBackup
@Databases = 'USER_DATABASES',
@Directory = 'C:\Backup',
@BackupType = 'FULL',
@Verify = 'Y',
@Compress = 'Y',
@CheckSum = 'Y',
@CleanupTime = 24


Then run the above script on SQL server agent job as per the backup plan strategy to execute this.

Also, just to mention you need to first create the scripts CommandExecute.sql and DatabaseBackup.sql in order to use the backup plan.