Yes, second part of those effects does not depend on the card actually being shuffled into the library. So the player would still reveal from chaos warp and draw from oblation.
However the one thing tha doesn't happen is the library won't be shuffled before those events happen. Since the only object to be shuffled into the library is instead put into the command zone the library won't be shuffled.
When a spell or ability resolves, it will do as much as it can. The shuffle part of each card is replaced with the Commander going to the command zone (so you don't shuffle at all, see relevant rules quote below) but you will still follow the rest of the directions of the card. Chaos Warp will still have the commander's owner reveal the top card of their library and put it on the battlefield if it is a permanent, and Oblation will still have the commander's owner draw two cards.
Quote from Comprehensive Rules »
701.16d If an effect would cause a player to shuffle one or more specific objects into a library, and a replacement or prevention effect causes all such objects to be moved to another zone instead, that library isn't shuffled.
However the one thing tha doesn't happen is the library won't be shuffled before those events happen. Since the only object to be shuffled into the library is instead put into the command zone the library won't be shuffled.