PCB Integrated Chip Question
Yes, you must connect all the IC's ground (and power) pins as required.

With some (most?) CAD systems there can be a problem wth "hidden" nets - power and ground pins often do not appear on the schematic, and are assumed to automagically connect to like-named nets.

I once experienced a missing ground problem with Protel due to hidden pins - the ground pins on a microcontroller were called "Vdd" (or maybe Vss - I can't remember which is equivalent to Gnd) and my ground net was logically called "Gnd", as I was using some bipolar TTL parts - the result was that the processor's "ground" pins were not connected to the rest of the circuit - result was no power on the processor - no work!!