There are studies that indicate they might. At least panther chameleons seem to: link

It makes sense to me to allow them the choice if they might be able to make use of the different areas.
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Torey
Eugene, Oregon, USA
1.1 Saharan Uros (Joe and Arthur)
3.0 Mali Uros (Spike, Turtle, and Tank)
1.1 Ornate Uros (Scuttlebutt and Shazzbot)
1.1 Collared Lizard (Ripcord and Rorschach)
2.0 Green Anoles (Bowser and Sprocket)
1.1 Chubby Housecats (Roscolux and Jenny)