Will pressure-treated lumber shrink enough to cause failure of roof flashing around it?
Wood expands and contracts regardless. It shrinks when it's sunny and it expands when it rains. Any flashing should be able to accommodate that, and I assume whatever was there before did so.
That said, vinyl post sleeves aren't terribly expensive. Even if your railings are bare wood, white, beige, or brown posts could look very nice. They'd also eliminate your contractor's concerns. They're worth considering.