Does a Vcc layer cause noise to a 4-layer RF PCB?
Planes are often used to ensure that RETURN paths are available for fast edges, to constraint radiation (for EMI control), to achieve clean waveforms. 

If your fast edges are from logic UP edges, then the logic VDD is providing high currents that will demand return paths.

You can use local and tiny ceramic capacitors from the VDD pin of the IC, to the GROUND plane. No need for that plane IMHO.

But you'll have to do a bit of thinking. And sketching the return paths. In exchange for this effort, you free up that "VDD plane" for many other valuable uses.