[mxmlnkn]

No, as far as I know, the pigz blocks, not to be confused with deflate blocks, are still compressed by referring to the preceding uncompressed data even if it belongs to another pigz block. Therefore errors would still propagate indefinitely in the worst case.

Other gzip variant formats like bgzip also make the chunks compressed in parallel completely independent. This results in ~3% worse compression ratio depending on the use case.

Note that another problem with bit flips and other errors in compression formats is that most decompression tool will simply quit on the first error even if the rest of the data could still be recovered.

Yes, bz2 is also more robust against errors because of the independent blocks.