Is it possible to have Preview add text at a place other than the center? Whenever I click the text tool icon, it automatically places a text box in the center of the screen. Is it possible to add text boxes at the location I click my cursor (for example at the left edge of my PDF)?

Any help would be appreciated.
Preview actually adds the text box at the center of the current zoom level and not the absolute center of the image, so you can manipulate the drop position of the text box by zooming on the region where you approximately want the text box to be dropped.

After that, you can quickly reposition the box with your mouse or by holding down Shift and an arrow key.

Changing the drop zone from the center to e.g. an edge, however, is not currently supported.