Is it possible to use the IVR component of 3CX without having to start the rest of the PBX? For example, terminate a SIP call directly to the IVR component to play an announcement.
No, it isn't possible. IVR is controlled by Call Manager, and doesn't have own SIP stack. You cannot make SIP connection to it.
Why do you need such an ability? Why not to reach IVR just as supposed thru simple call?