Assuming you mean the large battery, the answer is "no." The battery is essential for the hybrid system to go "ready" and stay that way. First generation Prius that have had battery failure sometimes had the failure show up when driving and the hybrid system just alarmed and shut down. The same thing would certainly happen to a later model Camry if the battery were to fail, but that is so rare as to be practically unheard of.
If you mean the 12 volt battery, I'm not sure. People who have tried disconnecting the 12 volt auxiliary battery once a Prius has started report all sorts of weird symptoms so the 12 volt converter is probably not very stable without a battery to settle it down. The Camry is going to be the same that way.
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