As I said, they do work offline but limited.
I know for sure since I've tested them.
Although nowadays a lot is done online, off-line protection is needed as well.
Think about portable media (usb stick, cd-r, dvd-r, external hd etc).
I can recommend to put (besides avast), McShield on that off-line system as well as Malwarebytes.
Haven't checked McShield, but Malwarebytes offers (just like avast) to download the definitions so you can install them on a off-line system.
The "minimum knowledge cache" is like the avast VPS.
Sure it has a lot of detections in it, but not the latest ones as they are not (yet) released but found in "real time".
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But why isn't the system online ?