You don't need the plastic dust cover per se, but you do need the top metal cup (which is the part that is drilled out) and associated rubber bushing pieces as it is what the bump stops rest against as well as the contact surface for the underbody body of the car. You won't be able to install the shocks without those pieces, but also your current shocks wouldn't work (assuming they're OEM) without those pieces.

The dust cover does help increase the life of the shocks as a whole to minimize contact with the shaft and reduce debris that may end up at the piston shaft entrance. The Konis do come with a plastic washer that sits right at the piston shaft entrance to reduce debris. I'm pretty sure someone on the forums did end up doing a Koni install without the dust cover.

My other vehicle does not have dust covers on its rear shocks, and its an offroad vehicle. The design is different though, with the shafts facing down rather than facing up. The shafts did needed to be replaced when the shocks were rebuilt due to pitting from road debris.