I don't see why not, a lot of people use bamboo in gecko tanks. Live or not, it should be ok, as long as it does't start rotting.
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Please Click the Dragon eggs/hatchlings!
you can coat it with polyurethane and let it dry really well to make sure the fumes are all gone and then it will last you just about forever and won't rot a bit.
There are also non-Voc sealers that you can get. what type of tree frog? you would be best to use a hardwood like oak or something as it will help establish the nitrogen cycle and moss like it a lot. you wouldn't even have to seal it!