Effect of redefining Avogadro's constant and kilogram on molar mass
Will these changes result in the molar mass of a substance no longer being exactly equal to the molecular mass expressed in grams?


Yes. The ratio between the molar mass and the relative molecular mass is called the molar mass constant, and it used to be 1 g/mol exactly. Now that Avogadro's constant is set to a fixed value, it's value has to be determined experimentally.

NIST quotes its value as 0.999 999 999 65(30) x 10-3 kg mol-1 (CODATA 2018).

The relative molecular mass of the carbon-12 isotope is still exactly 12 and the atomic mass unit u (or dalton Da) is still defined as 1/12 of the mass of a carbon-12 atom, so the relationship between relative molecular mass and molecular mass still holds. However, its molar mass is no longer exactly 12 g/mol.

As @MaxW says in a comment, these changes are so minute that they have no practical implications outside of metrology (which was one of the goals of the International Bureau of Weights and Measures when they suggested the change).