Yes it's possible but they will have to be horizontal stripes rather than vertical.

I've done it before it's easy as pie. I don't have time atm... but red velvet essentially is chocolate cake with red food colouring. It was originally made with really red cocoa, then alternatively beetroot juice. Now most people use food colouring. My favourite chocolate cupcake recipe is AWESOME just without the cocoa (I add more flour to compensate).

You could definitely colour white chocolate mudcake. Colouring batter is easy as pie. And layering is just as easy!