Should you blow through the final approach course if the ATC forgot about you?
Yes, blow right through it.  You should never deviate from a clearance to "take a beating" later simply because you think you know better than the controller.  If the controller is busy it is for a reason, and it is very possible they are extending you on purpose for spacing.  You could very well conflict with traffic even more by taking your own turn.  It is far better to let them fix the overshoot they caused than to battle the FAA over a flight violation.

If you genuinely think the controller may have forgotten about you, you should continue to attempt contact, while pressing IDENT with each transmission.  If it is so busy that you can't get a word in edgewise, press IDENT anyway.  I have done this and received an immediate turn without even having to transmit on the radio.  It is designed to get their attention, just don't overuse it.       

The only exceptions where you should deviate from an assigned vector are if you are lost comm or have an emergency.  In either case make sure you are squawking appropriately.  

I would consider a vector towards terrain a pending emergency if not turned within some appropriate period of time.  When I was instructing in the Navy, during simulator rides I would force a missed approach at McChord AFB, give a climb to 5000' and a left turn towards Mt Rainier.  I would then fail the crew's radios.  It was always a good lesson in terrain awareness, especially for young aviators from flat states.