If the sub woofer has its own amplifier (a "line level" input shows that it does), it does NOT put an extra "load" the main amplifier at all!
What happens is that the main amp. still "sees" your speakers as if the sub was not connected, OR gets gradually "disconnected" from your main speakers at a low frequency by way of a crossover capacitor being added to the main speaker path.
With a large capacitor being added to your main speaker line, the lower you go in frequency, the less of a load your main speakers have on the main amp.
This way, the sub woofer "picks up" the range your main speakers are "dropping off" via the subs speaker path crossover (if the sub woofer has NO crossover at the speaker terminals in\out, your main speakers just continue to play as they always do with the sub "brings up" the low bass, augmenting what your main speakers are doing).
It is a different story for a "passive" sub (NO electronics, NO line level input, NO AC cord connection), these units still drop off your output from the main speakers as you go lower in frequency, BUT through a large COIL, send your main amps output to the large sub woofers voice coil, and at the frequency that is in the sub woofers range, your main amp now just sees the larger speaker as your main speakers are dropping out.
This is like adding another larger woofer to a 2 or 3 way existing speaker system, you are adding more crossover parts to enable the "new" woofer to work with the existing system, even thought the "new" (sub) woofer) is in its own cabinet.
With a "powered" sub woofer, the load on your amp. remains the same at lower frequencies (or may be lightened if the sub has a crossover).
With a "passive" sub woofer, your amp. continues to be "loaded" even as you "go lower" and the sub takes over (as its crossover "rolls off" your main speakers while now putting power into the subs speaker.
If the (passive) sub has the same impedance as your main speakers, there should be no "overload" as the main amps "crossover" from your main woofers to the sub woofers.
On a powered sub, your main amp sees nothing "new" with your main speakers (a sub with NO crossover) OR sees less of a load as the frequency gets lower ( and drops your main speaker output ) as the sub "takes over".
None of the above applies (as far as amplifier load) if you are using the RCA line level inputs (passive subs need not apply here!)
Mark T.