Not without scripting.
Although you don’t need to script it from scratch, there already is a script that does that, something that’s part of a larger Pie Menu addon. Wazou’s Pie Menus.
He’s got it integrated as part of the TAB hotkey. It works for me what he’s got.
But if you still want the functionality that you described, then you can assign htokeys to the commands he calls in his Pie, as long as you have his addon installed!
For 1 you would use: mode.vertex
2: mode.edge
3: mode.face
If you don’t want to install his whole addon, you could grab just the file that has the Modes (pie_modes.py), activate it and setup your hotkeys.
Edit:
Just checked, the link to the thread I gave you is the old version of the script. For the latest one get it on his gumroad!