I see two flaws w/ that theory 1) while they are called squash bugs and prefer squash they will eat tomatoes, and every cuberit out there and watermelon, cantaloupe too. I have also seen them attack okra too so don't think they will starve w/o squash plants, and 2) I'm in your part of OK too and if you didn't plant any squash until now, try starting it in this heat and drought.We just pick them off and squash them them look for eggs on the underside of leaves and destroy those too. That's the only thing that I've found works with any reliability. I've been told waiting to plant them until now will interrupt their life cycle since they hatch at about the same time each year and if they have nothing to eat will die off. I'm going to try that next year and see how it works. Good luck.
Squishing is my first line, chickens my second line but they are fickle about squash bugs they aren't that fond of the flavor I think.