No, the resolution of the screen will not affect battery consumption. The reason for that is that, that the actual number of pixels is the same. The monitor cannot turn pixels on or off, as this would literally cause there to be little black spots visible on the monitor given that the pixel size is hardware based, and cannot be changed on the fly.
Note that if PPI is different but everything else is the same then the number of the pixels on the monitor is different and thus the power consumption will be different (the one with higher PPI will use more power).
The below is a more detailed explanation by analogy, to help give you an idea of how monitors actually work to virtually "scale" pixels. Note that the monitor still uses all available pixels, regardless of what it is displaying.
Zooming in too far
Think of how an image is scaled up or down on a computer screen. When you zoom too far in, it gets blurry, because the size of each pixel in the image begins to take up more than one pixel on the monitor.
To display the image, the monitor's pixel size actually does not change, but rather it begins to use multiple monitor pixels to display a single image pixel.
This means that the image has gained additional density, however the monitor has not gained or lost any density and is still displaying the same number of pixels.
Zooming out too far
To make the issue more clear, try to think about that in reverse. When you scale an image down too far, the monitor's pixels become larger than the the pixels in the image.
Imagine you scale an image down to half its original height and width. For the monitor to properly display the image, each of its pixels must represent four of the image's pixels (two in each direction, making a 2x2 square). The monitor does this by having the pixel display the color calculated by taking the average of the four pixels on the image that it represents.
This means that the image has lost some density, because the monitor does not have enough pixels to display the image in full at its current size. We say that "the monitor does not have enough pixels" because, again, pixels cover the entire surface area of the screen, and the number of pixels is limited by the size of the pixels.
To clarify, it is equivalent to say that the monitor's pixels are too big to display the image in the fullest possible quality at its current size, because the image's pixel density at that size is greater than the monitor's. The monitor still displays the image in the highest possible resolution, however, and still uses all of its pixels to display the image.
Have a look at this post about image quality and pixel density on Retina displays (2x HD quality of an ordinary HD display). It may help you understand how monitors will "scale" pixel sizes to match the content, while still using all available pixels on the screen.