You can direct output to a specific tty easily enough:
(
exec &> /dev/tty4
sleep 10;
python /home/pi/Desktop/execute_on_boot.py
) &
You should be able to see the output after you boot up with alt-ctrl-F4. There are 6 such virtual terminals (VTs), the GUI is running inside one of them, probably tty1 (alt-ctrl-F1).
You can scroll up in a plain text console with shift-pageUp, but it only retains what's appeared since you switched to that VT; if you switch to another one and back again, anything that's scrolled up is lost.
You could combine that with joan's logging idea by using tee:
python /home/pi/Desktop/execute_on_boot.py | tee /var/log/myboot.log