It's trivial to make tap water alkaline, as mentioned, so when I heard of alkaline water, I dismissed it. But I think Ray Kurzweil was a proponent, and I respect his views, in general. It would seem that food would completely overpower those relatively few ions in the water.
One way to really change the pH of your body is to use breathing techniques. It's only temporary, but it's apparently measurable. I've never tried measuring it, and don't even know how they do it, but if I understood what I read in some medical journal article and my memory isn't feeding me BS, it's a "thing".