Yes, but not officially (despite an in_joystick command) and it is not an ideal solution. 

If your joystick software supports mapping of standard key presses to each button and allows emulation of mouse movement you can use it in Quake4. 

Simply assign a key to each joystick button and enable the mouse emulation. Configure Quake4 using the in game menus.

If your joystick does not have software that enables you to map joystick buttons to key presses and emulate a mouse you may find the freeware program Joystick 2 Mouse of help.

Joystick 2 Mouse Homepage 
Joystick 2 Mouse Help