Yes, it can damage your camera.
Particularly, it can damage the sensor of a camera that does not have an optical viewfinder and that keeps the sensor exposed to provide an image on the LCD screen for composing photographs even faster than it can damage a camera with a mirror and optical viewfinder that protects the shutter curtains and imaging sensor from the Sun's light except for the instant the photo is actually exposed. Please note that even with a DSLR, when using Live View the danger is the same as with a mirrorless camera.
Lensrentals.com has posted a blog entry in which what happened to some of their rental equipment that were used without proper solar filtering during the recent total eclipse in the United States is shown in photos of the damaged equipment.
Damage to a shutter curtain:
Damage to a sensor:
Damage to the aperture diaphragm of a 600mm f/4 when the user used a rear positioned drop-in solar filter:
Thank goodness this camera wasn't in Live View and pointed directly at the sun with the shutter curtains open for the 1 minute it took the sun to do this through a 600mm f/4 lens. It happened during a flare test conducted by Bryan at The-Digital-Picture with the sun just out of the frame but obviously just inside the lens' image circle. If the light that fell on the edge of the light box had been focused on the sensor or shutter curtains (in viewfinder mode) the camera would likely have been rendered unusable.
The warnings almost all camera's manuals have against pointing the lens directly at the sun are there for a reason, and it isn't just so you can't blame the manufacturer when something goes wrong. Especially when the sun is almost directly overhead in a clear sky, the chance of damage is very real. The lower the sun is in the sky, the more clouds there are between the sun and your shooting location, or the more anything else (such as a proper solar filter) is absorbing some of the sun's energy the less likely it is that short periods of pointing your camera at the sun will result in damage. This is why it is fairly safe to take sunrise/sunset photos: due to the sun's angle it is passing through many more miles of the earth's atmosphere than when it is high in the sky.