Nope. Under the Cuban Constition everyone born in the national territory (this include the Guantanamo Base area) is a Cuban citizen except (a) children of foreign persons at the service of their government or international organizations, and (b) children of temporary residents.
Thus the children of US military personnel born in Guantamo are not Cuban citizens; although born in the national territory, they are born to foreign persons at the service of their government.
It’s an interesting question whether, if a Guantanamo detainee gave birth, the child would be a Cuban citizen. Plainly, the detainee is not in the service of their government. Arguably, they are a “temporary resident” of Cuba, although at this point their residence in Cuba looks more indefinite than temporary. Plus - I don’t know - temporary resident may be defined elsewhere in terms of the holders of certain types of Cuban entry visas or permits, whereas the detainees presumably hold no Cuban visas.
As to whether Guantanamo is “US soil”, Martin Hyde’s points notwithstandding, no, it certainly isn’t, and both the US and Cuban governments agree on this. This is not a position which the US adopted for convenience when they decided to open a concentration camp there; it has been their consistent position.
It’s true that the lease is indefinite, but it’s still a lease. The US has, and acknowledges, an obligation to pay rent. Plus, the terms of the lease restrict the purposes for which the US can use the base. Under the terms of the lease there are various things which the US government may not do on the base, and other things which they must do, and the US government acknowledges that it is bound by these obligations. None of these things are consistent with the base being “US soil”.