The service manual says the backlight runs at 30kHz 200VAC.
When the tube is lit, it could be dangerous. Maybe not lethal, but something to take into account so that you are aware of it and take care not to get a shock.
Without warning you don't expect to receive a shock from that part and the shock might scare you and you act on reflexes, which is not what you want when holding a hot soldering iron or sharp tools.
Usually these have circuitry to discharge any high voltage at some rate when turned off, but remember that the part might have failed and there might be some residual voltage left.
This circuit doesn't have a discharging circuitry though, but the other side of lamp driver output is connected to ground potential. The other side is driven via a 270 pF 2000 volt capacitor. So if it is off, it may not be a huge issue. But 200VAC at 30kHz I recommend not to touch.
Even if there was a charge left in the 270pF series capacitor, the capacitor is so small that measuring it with a multimeter that has absurdly high 20 megaohm input impedance would discharge the voltage down to 1% within 0.05 seconds or so.