No, the display can still be running and taking power even if the backlight is off.
The display has three major hardware components: a backlight, an array of colour filters, and an array of LCDs.
The backlight takes a lot of power, but is conceptually very simple: it just emits white light evenly across its area. The colour filters are complex (with red, green, and blue areas for each pixel) but fixed and don't take any power. The LCD array is equally complex, but also takes power: it has to filter the light differently for each pixel, letting all the light through for white pixels, blocking it for black pixels, and in between for other colours and shades.
So when the display is running, the LCD cells are working and taking power, even if the backlight is providing little or no light. (This also means that the graphics card and all the associated circuitry is running too.)
I can verify this from personal experience: I had the backlight die on a 2015 MacBook Pro. At first, I thought the entire machine had died. But after a while I thought of shining a torch through the apple-shaped translucent panel: and sure enough, it revealed a small patch of desktop background and the edge of a window — I could even see the pointer when I moved it across that area. That indicated it was just the backlight that had died.
So no, the LCD array, graphics card, and all the other display-related hardware and software &c can still be running and taking power even without the backlight.
This probably applies across most or all types of LCD display. (It's possible that some combinations of hardware and software may automatically shut down those things when you turn the brightness down to zero. But they don't in my case.)