Welcome!
Yes both methods should work. Don't worry about the second method draining power, it only "senses" the signal and still uses it's own power amp. Some prefer this method as it adds the sound of your power amp to the subwoofer. But it also requires an extra set of more expensive speaker cable versus interconnects output connections at the power amp that can handle two sets of connecting cables. Some subwoofers have high powered outputs so you can run the power for the loudspeakers through the subwoofer. Confused yet?

Doesn't make any sense to me.
Why does the extra set of speaker wires need to be more expensive?
Most amplifiers can be used with 2 sets of speaker wire even if there is only one pair of binding posts (especially if the wire used for the sub amp signal is relatively thin).
There are at least 3 ways to hook up a sub and main speakers with speaker wire and 2 don't require the main amp to have 2 sets of wires connected.
What is a "high powered output" on a subwoofer?