Following Abiwords help and man page, Abiword hasn't that option. You can force the geometry to your screen resolution but that isn't full screen mode.

Atril has that option, but you must specify a document to start in fullscreen mode. To open automatically on full screen from file manager, you can do a simple script like this:

#!/bin/bash
[[ -f $1 ]] && atril --fullscreen $1

and tell your file manager always open pdf and other files using your script.

Another solution, you can automate a key and mouse events using xdotool

try:

atril & sleep 1 && xdotool key F11
abiword & sleep 1 && xdotool key F11