Welcome gaba54 to FlyerTalk.
Calling SQ res is quite useless these days as they are all staffed by ningcumpoops located offshore!
But having said that, when you check in in Singapore, be sure that you have a copy of your ticket on ET that shows your flight number / date of your connecting flight to ADD. The check - in agent would be able to through check your luggage all the way provided it is within the legal connecting limit (which in this case, it is). But yes, you can only pick up your boarding pass in DXB when you go to the transfer desk. Be sure to show them the baggage tag.