no (in both directions). lots of np/exp problems paralize well and you can be in NC and parallelize really inefficiently (e.g. you can get a 10x speedup, but you need 1000000x the hardware). the better framing is that NC is the class of efficient algorithms that can be sped up near arbitrarily by parallelization
Hmm your last sentence seems to exactly agree that it's a class of algos that parallelize well? What does sped up arbitrarily mean? It's still polynomial speed up right?
It's a difference of degree. People expect something that "parallelizes well" to show near 1-to-1 speedup. Double the hardware, double the speed. This is "you can always speed it up, but the hardware requirements can increase at any polynomial rate".