The DOT has 3.5mm jack that allows for an external speaker(s) to be connected for a better listening experience. If your Bose unit allows for an external input, then yes you can connect the DOT to your Bose unit.
I have actually connected a soundbar, via the 3.5mm jack that I mentioned above, for a better sound. It works just fine.
It should be noted though that the sound quality that the DOT projects without any external speakers is very good on its own. No real need for any external speakers. They just make a good sound (device) even better.