Sure. A polymorphic worm can certainly use a "mutex" if it wants, to coordinate its activity. Nothing prevents it from doing so.
Depending upon what method it uses, this may provide a signature that signature-based A/V can use to recognize presence of the worm. Some of these methods may be easier for signature-based A/V to recognize than others. There are sneaky methods that a worm could use to coordinate between its instances that might not be trivial for A/V to detect.
For instance, one way that a polymorphic worm could coordinate its actions across all of its instances would be to communicate over the network with a command-and-control (C&C) server. The C&C server can track all instances and tell them what to do. Read about botnets for more. The C&C channel is a potential way that A/V can detect such bots, but there are also ways that bot operators can make the C&C channel stealthier, and ultimately this is a cat-and-mouse game.
I think the question you asked is of dubious practical relevance. Large-scale worms these days are passe. Instead of trying to infect millions of machines and get in the news, these days bad guys try to stay under the radar. Usually a much smaller botnet suffices, and it's not that hard to assemble one. Nor do they need sophisticated super-genius level exploits; given the number of poorly secured machines on the Internet, it's just not that hard for them to assemble a botnet with a few hundred or a few thousand compromised machines.