SUSPECT Status Of Databases, but Ola Hallengren backup job completed SUCCESSFULLY
Your problem was easily reproduced.  

I used the code in Creating a SUSPECT Database to create a suspect database on my local instance and then ran Ola's backup script.  The script executed without error (as you described).  The output did report the database as being suspect, but the script did not error.

Date and time: 2018-03-18 06:20:07
Database: [DemoSuspect]
Status: SUSPECT
Standby: No
Updateability: READ_WRITE
User access: MULTI_USER
Recovery model: SIMPLE
Encrypted: No
Differential base LSN: N/A
Last log backup LSN: N/A


In addition to not backing up suspect databases, there are (at least) Three cases where Ola Hallengren's Maintenance Solution won't backup a database.  

A Major takeaway from this post is:


  You should always always double-check either the msdb backup
  history
  or the master.dbo.CommandLog table to make sure any important backup
  was taken.


There are a variety of ways to query successful backup using the samples in Script to retrieve SQL Server database backup history and no backups.  An example would be to look for any databases that haven't been backed up today.

SELECT d.NAME
    ,bck.last_db_backup_date
FROM sys.databases d
LEFT JOIN (
    SELECT CONVERT(CHAR(100), SERVERPROPERTY('Servername')) AS SERVER
        ,msdb.dbo.backupset.database_name
        ,MAX(msdb.dbo.backupset.backup_finish_date) AS last_db_backup_date
    FROM msdb.dbo.backupmediafamily
    INNER JOIN msdb.dbo.backupset ON msdb.dbo.backupmediafamily.media_set_id = msdb.dbo.backupset.media_set_id
    WHERE msdb..backupset.type = 'D'
    GROUP BY msdb.dbo.backupset.database_name
    ) bck ON bck.database_name = d.NAME
WHERE bck.last_db_backup_date IS NULL
    OR convert(DATE, bck.last_db_backup_date) &lt;&gt; convert(DATE, sysdatetime())


My suggestion would be to add an extra job step to verify that all databases are being backed up and force the job to abend if a problem situation is detected.