Is carbon suboxide planar?
When we talk about a molecule being linear or planar, we only consider the positions of the nuclei and ignore the electron orbitals. Sure, &pi;-bonds might be out of plane, but that does not count. If it would be otherwise, we would have to consider that any atom except hydrogen has p-orbitals, and some of those are out of plane, and so no molecule ever would have the right to be called planar.

So yes, $\ce{C3O2}$ is kinda like an allene, with all its carbons having sp-hybrid orbitals, which inevitably makes the molecule linear and hence planar.

One might point out that the molecule is relatively easy to bend, but that's another story.