#hex power

From "The Return of the Blob" in The X-Men #7, September 1964. Stan Lee script, Jack Kirby pencils, Chic Stone inks, Stan Goldberg (?) colors, Artie Simek pencils. Photoshop color reduction.

Enough!

Billy is not a mutant and doesn't have an x-gene, so the short answer is no.

The slightly longer answer is that the text does not investigate the exact mechanics of Billy and Tommy's powers, and even prior to the retcon, it was actually a little vague about whether or not they were mutants themselves. I have always taken it as read that Billy and Tommy's powers are an exact duplicate of Wanda and Pietro's-- which, in the 2000s, would have meant that they were mutants. As I've said, the text supports the idea that Billy and Tommy are genetically identical to the original William and Thomas Maximoff.

For the majority of Wanda's publication history, she was considered a mutant, and this was still the case when Billy and Tommy were first introduced in Young Avengers, but our understanding of Wanda's mutation changed a few times over the years. In the late 90s, we learned that Wanda's probability-altering "hex power" is not actually her natural mutation. Per Busiek, Chthon altered Wanda's mutation to serve as a conduit for chaos magic, and her natural power would have been something elemental, similar to Magneto. Her "hexes," therefore, were an unrefined expression of raw chaos magic, and not a purely mutant power.

I typically prefer a more granular, distinct interpretation of Wanda's abilities, but the fact remains that her probability powers are not the naturally-occurring expression of her x-gene, and the same could therefore be said for Billy. In the current canon, they're not mutants, so none of this really matters.

Lately, I've seen some debate as to whether or not Billy's powers are fundamentally the same as Wanda's. I think they are. In the original run of Young Avengers, Heinberg intentionally sought to distinguish them by having Billy's powers manifest and express themselves very differently than Wanda's hexes. But at their core, both characters' powers are defined as chaos magic, and I think it's worth noting that since HoM, Wanda barely uses her classic hexes anymore. In practice, their abilities are very similar, especially in stories like Young Avengers (2013), which focused largely on reality warping, taking cues from HoM and Wanda's Nexus lore. Billy still uses the distinctive chanting gimmick, but I think that's meant to reflect the differences in their education and experience level, more than anything else.