The dealer will “try” to have Toyota pick up the tab?
Taking that TSB at face value, it clearly states that the problem will be covered by the Powertrain Warranty–but only if a customer complains about it.
As a result of Toyota’s own verbiage, there should be no question about this being a valid, covered warranty-related repair. If the dealer continues to hedge on the topic, then you need to “kick it up a notch” by contacting Toyota Customer Relations, via the toll-free phone number provided in your Owner’s Manual. Establishing a case number with these corporate Toyota folks will help to ensure that this repair is done at no charge to you.
Will your engine “die” if you decide not to have this free repair performed?
I can’t say for sure, but if there is a known defect in the camshaft drive gears and bearings, that certainly does not bode well for the long-term durability of the engine.
Since this will ultimately be covered under warranty (as long as you don’t continue to defer the matter), I have to ask–Why would you even consider not getting this free repair performed on your engine?