No, the ruling Communist Party doesn't pay any attention to it. Which is funny, because it was the Communist Party leaders left over after the Cultural Revolution that wrote the China's constitution and insisted that it was essential for the future success of Chinese society that it be obey. But China's leaders have been systematically disobeying the document since it was written. If China's leaders did obey it, however, a number of those freedom-hacking aspects of Chinese society would not exist. After all, the Chinese constitution is supposed to guarantee everything from ownership of private property to freedom of the press and assembly. The Great Firewall of China, as such, is total unconstitutional.
I'm no expert on the Chinese Constitution - I've never looked at it to be honest - but I wonder if it contains internal mechanisms that allow for it to be implemented. The theory underlying the US Constitution - as far as I can tell - is that no elected leader wants to follow it since it places constraints on their power. But they are forced to because those constraints (vetoes and the like) come from those in other constitutional offices.
Does the Chinese Constitution have anything like a system of checks and balances? If it gives power to one party - the Comunist Party - I bet it doesn't. Which would be a fundamental flaw.