Pink egg shell genetics are not well understood. I think
@AMERAUCANAS4REAL was looking into them for a genetics calculator (forgive me if I tagged the wrong person) so she(?) probably understands them better than anyone else on this site. I recall that she posted that the pink tint is the blume. Also, the egg shells are brown (not white), but not dark brown. Since there are a lot of brown egg genes, and they're not well-documented, it's pretty much impossible to figure out what one hen has.
So I imagine you'll get slightly paler eggs with a pink tint.
I think you may be interested in Croad langshan eggs? They're plum coloured, and very interesting looking. (Of course, the example below is probably from a highly bred flock far outside my budget range.)