No, they simply can't take the discoveries. The bomb-modifying discoveries listed in the class discription are a mistake and likely to be deleted in the errata (whenever tha'll be).
In short, those discoveries add effects to your bombs. But if you can't throw bombs to beginwith, the discoveries would have no effect even IF you'd take them.
The vivisectionist alchemist archetype replaces the bombs class feature with sneak attack, but lists a number of feats that improve bombs as feats that go well with the archetype. What happens if a vivisectionist alchemist takes one of these feats? Do they get to throw bombs that only have the feat special effects?
This was brought to the devs' attentions when the Vivisectionist was featured on the blog, but the book was already being printed. It will almost certainly be fixed in the first errata.
