Not quite. There can be more restrictions on the distribution or promotion of obscene material, but mere possession of obscene material is protected by the first Amendment: https://en.wikipedia.org/wiki/Stanley_v._Georgia

The reason why the Supreme Court upheld bans on possessing CSAM is not because it's obscene, but because it incentivizes abuse of children to produce it.

Stanley v. Georgia considered the question from the right to privacy side, not the first amendment. The relevant cases are https://en.wikipedia.org/wiki/Ashcroft_v._Free_Speech_Coalit... and United States v. Williams https://en.wikipedia.org/wiki/PROTECT_Act_of_2003#Supreme_Co...