No.
This was, indeed, a hoax.
* The real drilling was Kola Superdeep Borehole.
They didn't encounter any super-hot caverns (though the temperature reached a much higher than predicted 180 degrees C). There's no record of it ever being super-hot (the hoax claimed thousands of degrees) or emitting tortured screams.
* The hoax itself was well debunked, both on Snopes as well as Wikipedia.
The documentation included tracing first mentions of the story that were traced:
> he story was reported to first have been published in 1990 by a Finnish newspaper 'Ammennusastia', a journal published by a group of Christians from Leväsjoki, a village in the municipality of Siikainen in Western Finland.
>
> The story eventually made its way to the American Trinity Broadcasting Network (TBN), which broadcast it on the network, claiming it to be proof of the literal existence of Hell.