Yes. The core database is fully Apache 2 licensed with no strings attached: https://docs.yugabyte.com/latest/legal/. Maybe it will change if the company behind feels they're ripped off. Who knows, but for now, yes, you could.
CockroachDB has an explicit clause is the licensing: Yes, employees and contractors can use your internal CockroachDB instance as a service, but no people outside of your organization will be able to use it without purchasing a license: https://www.cockroachlabs.com/docs/v21.1/licensing-faqs.html....
