Thanks to Austin Whittall at the Patagonian Monsters Blog
Well, a paper: Mendez et al. The divergence of Neanderthal and modern human Y chromosomes. American Journal of Human Genetics, 2016 DOI: 10.1016/j.ajhg.2016.02.023,
States that Neanderthal Y chromosome didn't make it into humans.
The Abstract (full text is freely available) says:
Sequencing the genomes of extinct hominids has reshaped our understanding of modern human origins. Here, we analyze ∼120 kb of exome-captured Y-chromosome DNA from a Neandertal individual from El Sidrón, Spain. We investigate its divergence from orthologous chimpanzee and modern human sequences and find strong support for a model that places the Neandertal lineage as an outgroup to modern human Y chromosomes—including A00, the highly divergent basal haplogroup. We estimate that the time to the most recent common ancestor (TMRCA) of Neandertal and modern human Y chromosomes is ∼588 thousand years ago (kya) (95% confidence interval [CI]: 447–806 kya). This is ∼2.1 (95% CI: 1.7–2.9) times longer than the TMRCA of A00 and other extant modern human Y-chromosome lineages. This estimate suggests that the Y-chromosome divergence mirrors the population divergence of Neandertals and modern human ancestors, and it refutes alternative scenarios of a relatively recent or super-archaic origin of Neandertal Y chromosomes. The fact that the Neandertal Y we describe has never been observed in modern humans suggests that the lineage is most likely extinct. We identify protein-coding differences between Neandertal and modern human Y chromosomes, including potentially damaging changes to PCDH11Y, TMSB4Y, USP9Y, and KDM5D. Three of these changes are missense mutations in genes that produce male-specific minor histocompatibility (H-Y) antigens. Antigens derived from KDM5D, for example, are thought to elicit a maternal immune response during gestation. It is possible that incompatibilities at one or more of these genes played a role in the reproductive isolation of the two groups."
So the hypotheisis shown above of a distinct tree for Neanderthals is correct (the red tree exists and is different from modern humans Y chromosome haplogroups).
Also, besides mentioning maternal immune reaction against the hybrids, they speculate that Haldane's rule may have applied too.