Is it normal to drink water while peeing? to be more efficient?

You auto-replenish. I like you.

It's not normal if you do this to save time. Eating while pooping is not healthy at all.
I suggest you to combine other tasks which may complement each other like finalizing presentations while travelling to work.
I wish you best.

I don't bother to even drink it, just pour it straight down the toilet. Cut out the middleman.

I do it too. No eating while pooping though. I do however take a cup of coffee in with me.

Better to use that time in thought. Simple act of going through a bathroom door refreshes your mind and helps give you inspiration.