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Steam can also update and you also won’t get disturbed. If the issue is with your computer or a laptop/notebook you should try using the Reimage Plus Software which can scan the repositories and replace corrupt and missing files.
This works in most cases, where the issue is originated due to a system corruption.
It is not possible to prevent Steam client updates from being downloaded while the client is in 'Offline' mode.
There is a per-game setting which allows you to disable updates for individual games, which is accessible by right clicking on a game in your library, and selecting properties and choosing "Do not automatically update this game": It is worth noting that if you're playing a game on Steam, all Steam downloads are automatically paused unless you select the download option "Allow Downloads During Gameplay" (which is available through the Steam menu Downloads category, at the bottom), so you shouldn't experience Steam downloading files while playing Steam games.
Although this technique is very effective as Steam gets updated in the background while the user performs his tasks in the computer, it can also prove to be a nuisance for people who have metered/limited connections.