I suppose it depends on the pipe and maker.
I have a real Turkish block meer made by Hüseyin Ege and I have a composite/pressed meer from Royal Meerschaum.
The Ege meer you couldn't even tell it had wax on it, the wax layer on the outside was so thin. The RM meer had a wax layer so thick you could dig into it and see it on the pipe and made the pipe look as if it were a fake made of a white
on.
The Ege meer tasted fine from the beginning—the first few smokes were SLIGHTLY muted, but didn't taste off. No sour taste, no chalk taste, no milky taste, none of that. I know he boils them in beeswax (I've seen video on his official page on Facebook).
My RM composite meer basically just tasted like almost nothing, super muted, and having a slight waxy taste. After two smokes, I put some heat to it and then pulled a crapload of the wax out of the inside of the bowl and then it tasted normal.
These are my only meers and the only meers I have experience with, I'm hardly an authority on meerschaum. Just my anecdotal experience with two very different ones.