Specific TV engine question

For the most part, you'll just burn more oil. At some point it will plug or foul the catalytic converter. If fouled, you'll get a check engine light (CEL) because your downstream O2 sensor isn't seeing enough Oxygen consumed in the cat. If it's plugged you will slow to a crawl and wonder why you've run out of power. You could also get a CEL because of fouled sensors.

Another consideration for me would be the EGR system dumping oily exhaust back into the intake. This can foul intake valves, but the ported fuel injection will probably keep them clean enough.

I've run cars that used a quart per tank and I just added oil since it was cheaper than an overhaul. But those didn't have anything in the exhaust but mufflers.

Are you sure it's rings? I'd suggest a compression test to tell for sure. A set of valve stem seals might help a lot if it's not.

Eventually you will start fouling plugs and the truck will run poorly if at all, you will also be severely under powered.
Once you start smoking bad enough, if pride and concern for the environment does not stop you from driving,I'm fairly certain that most all localities have some law about driving a vehicle in that condition!