You can, but it's not a useful basis for comparison. The full pixel display area including borders for an Atari 8-bit system is 352x240. The 22:15 ratio that comes out of this is not generally useful, because most displays do not show this full area, nor can it be compared to broadcast specifications to determine how it will be nominally displayed. It certainly is not comparable to the 4:3 ratio that is frequently used to try to fit retro system displays.

The pixel aspect ratio is not affected by how large the active display region is. Displays can't even detect the border if the border is at blanking level black as older systems tend to do. It's determined by the horizontal/vertical timings and the pixel clock. Those can be compared to the specifications for NTSC/PAL square pixels to calculate the resulting display size and aspect ratio on a standard-tuned display for a given image pixel size.