I was really wondering this because in the script, Palmer burns Child's weed farm fearing that the plants were assimilated. If it can assimilate plants, how would the organism go about doing it? Quotes: "Don't get near 'em. The plants! They're alive. Those things can imitate anything..." "Palmer sprays them with flame."
Given that scene (and any others involving the pot farm) didn't make it into the film, its canonicity is highly suspect. But in any case, Palmer's opinion (if he had not been infected at that point) is nothing more than a guess about what might or might not be possible. "Better safe than sorry" is a good attitude to take under such circumstances.
Based on the film, the answer is that we just don't know. We have no idea what the Thing is ultimately capable of. When questioned about its capabilities, McReady puts the matter succinctly:
I don't know how. Because it's different than us, see? Because it's from outer space. What do you want from me, anyway?
(If I had to guess though, I would bet that if an alien could manage to metabolize or infect Earthly animals, plants should not be much trouble; plants and animals ought to be a lot closer than animals and aliens.)