If a static charge is big enough, yes it can travel through an insulator like plastic. Lightning is a static discharge. its voltage is just high enough to ionize miles of air (strip the electrons from the atoms to polarize it and make it conductive). It will jump right through things you normally consider an insulator like car tires or shoe soles (otherwise cars and people would never be struck by lightning). An insulator does not prevent the flow of electricity, it just has a high resistance to the flow of electricity per length.
You're highly unlikely to build up a static charge this large in your body, for the simple reason that it would dissipate through your shoes or the carpet into the ground first. It is possible to develop a charge this large if you're separated from the ground (e.g. in a helicopter, which is why workers dangling from a helicopter always use a grounding strap or pole - so the discharge goes through that instead of their body).
The ground plug on the computer is there to protect you, not the computer. If there's a wiring problem and the 110V AC somehow gets sent to the case, it'll be discharged through the ground plug instead of you when you touch the case. A static charge in your body will discharge to a metal case regardless of whether the computer is plugged in. You develop a static charge in your body, and when you touch the metal case that charge tries to spread evenly through your skin's surface and the metal case. The metal case has sufficient mass and conductivity to absorb the majority of that charge, grounded or not. This is why you can discharge static into a metal doorknob even though it's supported by insulating wood on all sides. The grounding does mean that it can continue to absorb static discharges indefinitely, but makes little to no difference for the occasional static discharge.
Yes static can build up in a plastic case. But when static builds on an insulator like plastic, it cannot travel along the surface and thus doesn't discharge through a single point of contact. e.g. You rub a balloon on your hair to give it a static charge and stick it to the wall. If you touch a metal rod to it, it'll continue to stick to the wall. The rod absorbs the static charge only from the part of the balloon it touched, not the entire surface of the balloon. Your body is different - since it conducts electricity, touching a metal object causes the static charge over your entire body to flow through your body to the discharge point. To eliminate the static charge from the balloon, you have to rub the metal rod (or your hand) over every part of the balloon you rubbed on your hair.
The part about the case forming a cage which protects the components inside from static discharges to the case is correct.