Is old networking still in the Unity Engine?

If I will update Unity to a new version containing UNET, can I still use all the functions from the old networking before UNET?

Yep, all the scripting functionality is still there and you can find the “Network View” component in “Miscellaneous > Network View”.

I’d say that it isn’t likely to disappear soon, assuming it doesn’t conflict with the new networking features as the old particle system is still included too.