In cameras that have a mechanical shutter, which are the only cameras I am aware of with shutter durability ratings, the answer is, "Yes, using Live view will increase the number of shutter actuations."

This is because the shutter does not normally stay open continuously on such cameras when shooting in Live View. What happens when you press the button to take a picture: Shutter closes to block light from striking the sensor-->Sensor resets the photon count at each 'pixel' to zero-->Shutter opens to expose sensor to light-->Each 'pixel' counts the number of photons that strike it-->Shutter closes to block light from striking the sensor-->The data from the sensor, how many photons struck each 'pixel', is read-->Shutter opens to allow light to strike the sensor so that a Live View image can be sent to the camera's LCD. And that is the simple version.

With a typical two curtain focal plane shutter, each shutter cycle includes the first curtain opening, the second curtain following it across the focal plane to close it, and then both curtains traveling back across the focal plane while still overlapped to reset them to their starting positions. When using Live View, the 'starting position' is modified to be with the first curtain already open. When the second curtain closes then both curtains are reset and the first curtain opens to take the picture. Once the exposure has been made, the shutter cycles again by closing the second curtain, resetting both curtains, and opening the first curtain to return to Live View.

So for cameras that operate this way, each Live View session includes two shutter actuations for each image recorded plus one more for the open/close/reset that results from starting and ending the Live View session. If you were to start Live View, take seven exposures, and then end Live View you would actuate the shutter a total of 15 cycles: (7*2)+1=15.

For cameras that allow an option to use electronic first curtain when using Live View (or an electronic viewfinder which is essentially Live View), The number of shutter actuations will only increase by one for each frame recorded plus one additional actuation per session.

There are some mirrorless cameras that take high speed bursts without actuating the mechanical shutter in between frames. Essentially what they are doing is saving each frame of video as an individual image. But I know of no such cameras that have shutter durability ratings, although I haven't specifically searched for such a camera that does have a shutter rating.