The image of the beast is mentioned in passing in Revelation 16:2. The first bowl-plague falls on those who worshiped the image of the beast. Babylon is parallel to the Great City in 16:19, but no direct connection is made within the chapter between Babylon and the image of the beast. However, there are strong parallels between Revelation 16:13-16 and Revelation 13. Revelation 16:13 picks up on the motif of an unholy trinity, which work together in both passages for a common cause, to cause the inhabitants of the earth to worship the beast and its image (Rev 13:8, 14, 15). In order to achieve that, the dragon gives his authority to the sea beast (Rev 13:2). The land beast exercises its authority in behalf of the sea beast (13:12). The land beast then breathes life into the image of the beast (13:15). So there is a chain of authority running from the dragon to the image of the beast.
An additional parallel between Revelation 16 and 13 is the mouth motif.
The three frogs come out of the mouths of the dragon, beast and false prophet (16:13). Earlier, the dragon uses its mouth to accuse the faithful before God (Rev 12:10). Similarly, the sea beast uses its mouth to speak blasphemies (Rev 13:5), the land beast uses its mouth to breathe life into the image of the beast (13:15), and the image uses its mouth to order the death of all who will not worship the image (13:15). Through all these mouths, the dragon is able to gather the inhabitants of the earth before the image to worship it. A further parallel between Revelation 16 and 13 is the concept of worldwide deception through miraculous signs (Rev 16:14; 13:13-14). The demonic spirits work signs to lead the rulers of the earth into battle against God (16:14). In Revelation 13:13-15, the land beast/false prophet uses miraculous signs to gather the people of earth for the worship of the image of the beast. These passages (16:13-16 and 13:15-17) also share a number of verbal parallels with scene on the Plain of Dura in Daniel 3.
This all suggests that while the Battle of Armageddon makes no direct reference to the image of the beast, whether or not to worship the image is a part of that spiritual conflict. The worldwide worshiping of the image of the beast is likely the same event as the worldwide gathering for the battle of Armageddon, in which Babylon falls (Rev 16:16, 19). Revelation 13 and 16, then, are describing the same eschatological event, the last worldwide deception concerning worship. People are making decisions whether to worship God (Rev 14:7) or worship the image (13:15-17), someone/something other than God. Since Babylon is mentioned in the context of Revelation 16 and the image of the beast is mentioned in the context of Revelation 13, it is very possible, even likely, that Babylon and the image of the beast are one and the same entity.