I don't think you're quite understanding the idea of secession. If a state decides that things are so bad and they decide to seceed, they no longer acknowledge the laws of the United States, making a US law against secession a moot point.
The point of the law is to make it very clear that secession will be met with an invasion and a reclaiming of the state (s) and it's people. That however is a separate issue entirely from States being "allowed" to seceed. Of course they can, but the consequences most likely wouldn't be worth it.
Ironically, false.