No, using that power plate with your Bose system is not a good idea. Your Bose subwoofer not designed to be used with a power plate and will not work properly with one. The power plate is designed to be connected directly to an appropriate speaker driver (the actual moving speaker inside the subwoofer). It's not meant to be connected to the 5 speaker crossover that your Bose subwoofer has in place before the driver.
Despite what others have told you in this thread, your Bose speaker system, the entire speaker system with all of it speakers, is designed to be connected to the 5 speaker terminals of surround sound AV receiver. When connected properly, with 5 speaker cables running from an AV receiver to the Bose subwoofer and the 5 speaker cables connecting the matching Bose speakers to subwoofer, the entire speaker system looks and behaves like 5 seperate full-range 8 ohm speakers. This is what an AV receiver is designed to handle.
Note that Bose speakers systems are very poorly regarded here. Regardless of the fact if used properly it will work without risk of damage to anything, it's sound quaility is never going to be good. Used improperly it's going to sound even worse, and you do risk damaging your equipment. You should really give up your idea of using it in your second zone. Get a new set of speakers, do not try to connect the Bose satellite speakers directly to your receiver, this is much more likely to cause serious damage, and get a powered subwoofer with speaker level input and outputs if you need more bass. You could also get a 2 speaker Bose system if you want, but this is probably not your best option in terms of sound quality.