To answer the broad question, yes,
some BSDs (FreeBSD) support
some laptop hardware[0] as well as Linux does. And yes, the battery life is comparable. FreeBSD has good support for idling in C-states, which is where most of your CPU power saving comes from; support for setting and managing P-states (which no longer have much impact on modern Intel CPUs, but mattered historically) via e.g., "powerd;" and support for wifi power saving modes and screen dimming (other big power draws).
The question that was sort of implied but not directly asked might be: if you pick a random laptop, do I think it's likely a BSD will support it better than Linux? And there I think the honest answer is "no." Linux definitely has an advantage in breadth of driver coverage.
In many ways FreeBSD is a well-kept "secret," but it's not a panacea.
[0]: https://wiki.freebsd.org/Laptops