Can conjunction reduction be applied with "so"?

The following examples of conjunction reduction sound wrong to me; are they grammatically correct?

The meat is red, so is raw. [The meat is red, so it is raw.]

The fish is pink, so is a salmon. [The fish is pink, so it is a salmon.]

Maybe my discomfort comes from the proximity with this other "so" (adverb) construction:

The meat is red, so is the wine.

The fish is pink, so is the rose.