Voxel Cone Tracing in Deferred pipeline?

Is it possible to run cone tracing shaders over a fullscreen quad and sample vertex data from the GBuffer or is that generally a stupid idea?

Yes, however that's not voxel cone tracing anymore. That's Screen-Space Global Illumination (SSGI) instead. You can think of the voxelized scene in VCT as a 3D GBuffer, which makes all the difference between "screen space" and "full scene".

Do I lose accuracy because I only have per pixel vertex data?

Absolutely. All screen space approximations suffer from the same set of artifacts. They do not account for surfaces that aren't directly visible on the screen (either out of frame or occluded by visible geometry). Most noticeably, when the camera moves and objects enter or exit the frame, the reflections on visible surfaces would also change unrealistically.

A question is perhaps, what's your motivation for trying doing both.

When you do Voxel Cone tracing you are trying to solve the exact same problem you would be trying to solve with deferred rendering and now have the overhead of both techniques, if you are already willing to deal with the overhead of Voxel Cone tracing then it's better to fully commit to that technique.

The reason is simple, if you are doing voxel cone tracing then you have a 3D texture of some sort (could be voxel oct tree, and actual 3D texture or some other structure). That is essentially a 3D Gbuffer.

If your idea is simply to eliminate the need for such a structure and use the existing planar GBuffer instead, then you are introducing artifacts that do not appear with traditional SSRT techniques.

In essence trying both at the same time is likely to give you the worst of both worlds rather than the best.