VirtualBox and VMWare use virtualized graphics cards, yes. You won't see your actual card listed at all, just whatever generic virtual card+drivers the VM uses.
That said, I couldn't get D3 running on VBox because of lack of GPU support (they don't have a set of guest tools that help like VMWare does edit; they have guest tools but D3D support is limited, I mean).
If you install the Guest Additions and check the experimental D3D support box you *might* be able to get to the character profile screen and Auction House, but it'll be flaky at best.