Good question - I would suppose that it would as the system is generic and not specific, as on a cars alarm. Taking that query to it's ultimate scenario - should you be sat next to another bike/mobility scooter with the same system, you could start their indicator off as well!!
I would suggest, not trying to deactivate the siren. How many times have you been out on the road and thought the car driver in front that hasn't cancelled his/her indicator is an idiot, this could be said of you if you were to leave the indicator on or you could find that a car pull out and have you off your bike, because he/she thought you were turning. So in all truth I would say, just leave as is, you being safe on the road is more important than a little annoying siren sounding. Happy cycling.