I don't understand why servicing a dollar-denominated debt causes an increase in aggregate demand. Sure, you need to buy dollars, but when you pay the debt, now the person on the other end gets them and puts those dollars back in the market.
But the market is made up of independent actors all of whom want to make sure they get the dollars they need first. It's like a rush for the fire exit with everyone jammed at the door instead of an orderly line.