Standard cargo bays can't launch other units, so you could carry the DropShip, but you couldn't launch it in to space (in one piece). A DropShuttle Bay can launch, but has a tonnage limit to the shuttles that can fit inside. Unless you want to disassemble your DropShip, load it in a cargo bay, remove the individual pieces from the cargo bay using a smaller shuttle, and then reassemble your DropShip, you'll want a DropShip collar for your DropShips.
(SO p. 43 has the rules for unloading cargo from a bay: it requires a docked aerospace unit, or the transport to be grounded. Since a WarShip can't ground itself, you need to use a docked aerospace unit. And unload from the WarShip cargo bay to the docked aerospace, then launch that aerospace. There is no way to directly launch cargo into space, certainly not of large DropShip size.)