It is generally recommended to disable the cloud for this game.
Whether you are in offline mode or online mod is pretty irrelevant really. Steam is a pretty stable platform, and I don't think issues occur that often, especially if you play in career mode.
As for Game Save Manager, make sure that you use multiple backups, and not just one. If your F1 2013 game save profile gets corrupted, then there is a good chance that your single backup may be corrupted too.
This is the problem with Steam Cloud. The corrupted profile gets saved to the cloud, overwriting any previous good profile.
I use scheduled game save manager backups, which creates a new archive every time that an actual backup is made. If there has been no change to the profile since the last backup, then no backup is made.
This means that if corruption occurs, you can step back through the backups until you find the last uncorrupted one.
Here is my GSM settings for a Daily Scheduled Backup. You can see that they not only go on a backup drive, but the folder is also within my Onedrive (Skydrive) folder, so will be uploaded to my cloud.
As you can see from my backups, it's been a while since I have played the game, so no new backups are made, even though the schedule runs daily. My game saves from other games are backed up though, but to other folders within that 'GameSave Manager' folder ......
Cheers