Yes, it’s possible. Many older flashes use much higher trigger voltage than modern DSLR hot shoes are designed to handle. That voltage can be present as soon as the flash is powered up and charged, so damage can occur even if the flash never actually fires.

If the old flash was off or not charged, the risk is much lower. But if it was powered and ready, it could have damaged the camera’s flash-trigger circuitry. Your symptom—where a known-good Canon flash works on another camera but not on the T3i—does fit that possibility.

The damage is often limited to the flash interface/trigger circuit, so repair may be possible, but cost depends on the extent of the failure. The best next step is to stop testing random flashes on that camera and have Canon or a qualified camera repair shop inspect it.

For future use, check the flash trigger voltage before mounting older flashes directly on a modern camera, or use a safe trigger interface/adapter.