Hhmm... never thought of that. Never really had a desire to build something like that for the Atari 2600 since, IMO, the 2600 is a home console, not an arcade.
All opinions aside, according to the pinout schematic, that does seem like a possibility.
The joystick pinout is:
1     WHT  <--     Up
2    BLU    <--    Down
3    GRN    <--    Left
4    BRN    <--    Right
5    n/c    -    Not connected
6    ORG    <--    Button
7    n/c    -    Not connected
8    BLK    ---    Ground(-)
9    n/c    -    Not connected
The paddle pinout (different source) is:
1    NC
2    NC
3    2P Fire
4    1P Fire
5    1P Paddle (X-axis)
6    NC
7    +5v (pot common)
8    Ground
9    2P Paddle (X-axis)
As you can see pins 5, 7, and 9 are unused on the joystick, but used by the paddles. The only pins that are shared are 3 and 4 for the Left/Right <-> Fire1/Fire2 controls. Wiring multiple buttons that way is trivial.   
However, while it seems mechanically possible to merge the controllers since their pinouts don't seem to interfere, I have no idea how any of the games might react to accidental inputs. For instance if a drunk buddy decides to push up on the joystick while you're playing a paddle game. Or whether a joystick game might react to input from the paddle.
I say give it a shot and see how the games react, just don't kill off an old joystick or paddle to do it. 
