And just forget about the invasion film with Nicole Kidman. Bring back the damn pods! And I want to see this thing spread GLOBABLLY. And see how people in different countries react. Someone will likely develop a way to neutralize the aliens that hasn't been thought of before. Should be interesting!
Actually, Kevin McCarthy appears in the seventies movie as the same character at the beginning of the movie screaming about body snatchers. So technically it is indeed a bit of a sequel.
He's not literally playing the same character though. In the strict context of the 1978 movie he's just some guy being chased by pod people.
In a "meta" sense though, McCarthy's cameo creates the impression that Miles Bennell from the original has managed to escape the bounds of his movie and run on to the set of the remake to warn his alternate universe self about what's going to happen. Then he promptly gets killed, foreshadowing the fact that this time the character (now played by Sutherland) isn't going to make it out alive. McCarthy's character is like a ghost from the past and a time traveler from the future at the same time.
So you could say the 1978 version is a spiritual sequel or companion piece to the 1956 version.