Yep, he is. He is a CoM in the Baskerville Household and he is also labeled as a Baskerville (as well as a Nightray) in the 18.5 Evidence Guidebook (the same as Gil). Zai, who seemed to have been an Unofficial Baskerville, was only shown to be a Vessalius and not a Baskerville at all.
However, Baskervilles aren’t immortal, they are just difficult to kill by normal means because they are more Chain than human. This means that they could be killed by Mad Hatter, which kills other Chains and was how Fang died. They can also be killed by beheading (hello there Oswald!) or by being sacrificed to the Abyss in the Glen Succession Ceremony (though this only applies to Baskervilles who are also CoM). The last way we definitely know that they can die, is by their body rotting away due to the power of the Abyss residing in them, though this only appears to apply to Glens (who have five Chain contracts). They then transform into Chains, so in a way, they are reincarnated.
Other than those ways though, Baskervilles can’t really die.