The blue colour in blue Powerade is a dye called FCF blue synthesized organically for food dyes. It contains an organic compound Triphenylmethane as a back bone. The colours in most chical compounds is due to the oxidation state or structural formula.
When you drink the Powerade, the compound is synthesised into a different compound in your body therefore losing its blue colour.
It by no means stain your insides because the body can synthesise like any organic food. Infact it is no different from the blue berries you eat. And yet when you eat the blue berries your insides stay the same.
Colour is a qualitative nature of chemistry. It's an indicator of what chemical changes take place. Whether it be organic, inorganic or physical chemistry.
I don't think it's the Powerade though. Most of waste from the Powerade, would have passed as urine. I think I will not say anymore because the next things I say might be personal.
I would say though that there is no cause to worry.
You seem to take your health and fitness seriously. You know what, I will say no more. This is a public space.
Since it is just a coloring and isn't really blue, it gets dissipated throughout your system, mainly your bone structure because food colorings usually have gelatin in them.
Superb Opinion