Not quite. We're a common law nation and the courts have defined what obscenity is. Sort of. And it isn't what you probably think.
The Miller Test
Something may be considered obscene only if all three apply:
(1) The average person, applying contemporary community [local] standards, would find that the work, taken as a whole, appeals to the prurient interest
(2) The work depicts or describes sexual conduct in a patently offensive way [specifically defined by applicable state law];
(3) the work, taken as a whole, lacks serious literary, artistic, political, or scientific value. [This branch of the test is based on national, not local, standards.]
~ ~ ~
Profanity is something else entirely. It is going to be covered by the 1st amendment. See Cohen v. California (Supreme Court said that the message "F*CK the Draft" in big letters on the back of a man's jacket was constitutionally protected political speech.)
Justice Harlan's arguments can be constructed in three major points: First, states (California) cannot censor their citizens in order to make a "civil" society. Second, knowing where to draw the line between harmless heightened emotion and vulgarity can be difficult. Thirdly, people bring passion to politics and vulgarity is simply a side effect of a free exchange of ideasâ"no matter how radical they may be. --wikipedia
Basically, if South Carolina's law could conceivably be applied to censor such speech (which, duh, it certainly can) then it will be unconstitutional for broadness, among other things. If this thing somehow miraculously makes it into law, the Federal Courts will not take kindly to it.