No. Plains remains at one production and hill remains at two. However, I didn't get everything right in the above post:
Flatland cities (no matter if plains or grassland or flood plains) start at 3

/1

if on a fresh-water tile (Lake, River, Oasis) and 2

/1

/1

if on a non-fresh-water tile.
Hill cities start at 2

/2

no matter whether there is fresh water or not.
So, in short, every city has at least 2

/1

and gains either 1

(if on hill) or 1

(if not on hill and having fresh water) or 1

(if not on hill and no fresh water).