Do nucleosomes ever completely unwrap during transcription?
Yes, nucleosomes are completely unwound. Histone chaperones such as FACT (for H2A/H2B) and ASF1, CAF-1, HIRA, Nucleophosmin etc (for H3/H4), associate with RNA Pol II and handle the displaced nucleosomes. As you surmised, the histone octamer complex is disassembled, into the H3/H4 tetramer and two H2A/H2B dimers. Right behind the elongating Pol II, the chaperones reassemble nucleosomes. During the process of reassembly, it has been shown that "new" H2A/H2B dimers (and possibly H3/H4 tetramers too) can get incorporated into an "old" histone octamer. Finally, nucleosome remodelling complexes such as SWI/SNF re-space the nucleosomes.

This is a decent review of the process (by one of the discoverers of the FACT complex, incidentally): "New chaps in the histone chaperone arena". Campos &amp; Reinberg. Genes &amp; Development (2010): 24: 1334-1338

This is a comprehensive review of histone chaperones and nucleosome dynamics during various DNA-dependent processes (such as transcription, replication and repair). There is an entire section on their role in gene transcription, which is the main thrust of this question: "Histone Chaperones: Assisting Histone Traffic and Nucleosome Dynamics". Gurard-Levin, Z.A., Quivy, J., and Almouzni, G. Annual Review of Biochemistry (2014): 83: 487-517

And finally, a good overview on histone dynamics and chromatin structure during transcription: "Histone exchange, chromatin structure and the regulation of transcription". Venkatesh &amp; Workman. Nature Reviews Mol. Cell. Biol. (2015): 16:178–189 



I should add that an inability to disassemble nucleosomes (or displace any other factor bound very tightly to DNA) can actually pause an elongating Pol II complex.