I am in great delima . I have performed one POC to see if there is any impact on backup of running Azure VM if C drive space of VM is full. As expected it took the backup successfully. What i understand that Azure considers VHD's as file and which has nothing to do with C drive space of VM for taking backup.
But for other server whose C drive is full and backup service tries to take backup, it didnt happen. I have noticed that snapshot extension runs intermittently on Azure portal. Even upon refereshing the extensions, it didnt work.
No logs have been found which says backup failed due to C drive space, neither anything related to VSS & IAASVMProvider.