Will VSS backups break logchain?
You could verify the backup history with the following script:

SELECT  
   CONVERT(CHAR(100), SERVERPROPERTY('Servername')) AS SRVNAME, 
   msdb.dbo.backupset.database_name,  
   msdb.dbo.backupset.backup_start_date,  
   msdb.dbo.backupset.backup_finish_date, 
   msdb.dbo.backupset.expiration_date, 

   CASE msdb..backupset.type  
       WHEN 'D' THEN 'Full'  
       WHEN 'I' THEN 'Diff'
       WHEN 'L' THEN 'Log'  
   END AS backup_type,  
   msdb.dbo.backupset.backup_size / 1024 / 1024 as [backup_size MB],  
   msdb.dbo.backupmediafamily.logical_device_name,  
   msdb.dbo.backupmediafamily.physical_device_name,   
   msdb.dbo.backupset.name AS backupset_name, 
   msdb.dbo.backupset.description,
   msdb.dbo.backupset.is_copy_only 

FROM   msdb.dbo.backupmediafamily  
   INNER JOIN msdb.dbo.backupset 
   ON msdb.dbo.backupmediafamily.media_set_id = msdb.dbo.backupset.media_set_id  

WHERE 1 = 1
ORDER BY   2,3 desc


The script will give you an overview of the backup media and files and if you look at the last column is_copy_only you will see if the backup is COPY_ONLY (1) or not (0).

If they are COPY_ONLY then they will not break the backup chain. Otherwise you might face issues as explained in the following article: 

COPY_ONLY Backups with SQL Server  


  Starting with SQL Server 2005, a new backup option has been added that allows you to take full and transaction log backups in between your regularly scheduled backups without affecting the LSNs and therefore the sequence of files that would need to be restored.  Since Differential backups backup all data pages since the last full backup, these types of backups do not affect the LSNs and there is no difference when using the COPY_ONLY feature.


You might want to check out my answer here which was posted in response to the question How can I backup an SQL Server database using Windows Server Backup?.

It is related to Windows Server Backup and VSS, but touches on some points you might encounter with the VSS backup strategy that has been implemented at your shop.