Now I can reply to this question. I guess we can't have too many nested replys.
I actually haven't tested having the alarm go off with an external speaker like that. But, when I'm using headphones it will actually play on both the headphones and the phone's speaker. But when I pair my phone through the Amazon Echo Dot that I have, the alarm plays on the dot and not on the phone. I'm actually not entirely sure why that happens, but I think that has to do with how android manages audio. But anyways it should be fine, but your mileage may vary.