Taking B vitamins isn't going to cause a mass concentration of RBC. The only way you have a concentration the way you describe is through dehydration, Gotap. It's called hemoconcentration. You are right about what you describe, but you just have the reasoning behind it wrong.

Athletes train at altitude to induce polycythemia to increase their RBC count so when they go back to sea level, they have an increased ability to transport oxygen. R2L is right in saying the danger lies in the HCT levels, not the actual RBC levels themselves.

But you, nor your dog, are gonna develop life threatening polycythemia from B vitamins.