They will certainly try, but they don't have the capability yet
It's probably a really bad idea to keep building them autonomous killing machines though
Hyper proliferation of drones seems to end in a state of mutually assured destruction, from my armchair.
I wouldn't be surprised if multiple nation-states already had them without calling them such because 'Look, someone pushed a button 3 hours ago before it engaged'. Once the private capital gets their hands on them, we immediately transition to cyberpunk no matter what else happens in the world.