No. It is not possible to provide a VirtualBox VM access to the host video card, only the virtual interface you see listed there. In fact, this is true for most hardware including network cards as well. The primary exception to this is some USB devices and storage controllers that can be revealed to the VM if the host OS is not using them via a special bridge driver.
Using a Linux distro in a VM should give you a feel for whether you like the software or not, but it is not a good test of whether it interfaces well with your hardware.
Instead you should use a LiveCD or bootable USB release to start it up with full access to your hardware. This will allow you to test all the things you want to checkout without over-writing or re-partitioning your hard-drive until you think it's going to work.
As a final note, most Linux distros share relativly the same base of drivers and hardware compatability. How well they juggle it all varies some, and sometimes one distro will have work-arounds for certain machines that have not made it into the upstream projects, but it's pretty safe to say that if your video card and display works in one Linux distro, it is likely to work in another distro of the same era.