Yes, this can be done.
Install xbindkeys
:
sudo apt-get install xbindkeys
And create the config file:
touch .xbindkeysrc
And now edit the file:
gedit .xbindkeysrc
Add this to the file:
"gnome-terminal -e 'sudo apt-get upgrade'"
Control+1
Save the file.
Now you need to add xbindkeys
to "Startup Application". That is addressed near the bottom of this answer on remapping keys.
The only problem with this solution is, if there aren't any prompts, the terminal will only stay open long enough to get your password and ask if you want to run the upgrade. I don't know of a way to keep the terminal open, but maybe someone else will.