What percentage of physically mature women grow measurably taller
during pregnancy?  I have heard cases of women gaining an inch in
height, presumably because of hormonal changes.

unless pregnancy occurs before full maturity, there really is no way
to increase height after the bones are fully formed and the growth
plates have gone away, which happens in late teens or early twenties.
If the person is still growing, it would presumably continue during
pregnancy. However, for the fully mature woman, if anything one might
expect slight shrinkage as the hormone effects which allow for
stretching of the abdomen and pelvis take effect.

One addition to my comment above: it's conceivable that a woman could
simultaneously be pregnant and have a growth-hormone producing tumor
of the pituitary gland, which could cause growth. This would be
unrelated to the pregnancy per se.