Imagine you are mopping your kitchen floor. It has rained outside and you've tracked in a bunch of mud. You put nice clean water in a bucket, add some detergent and start mopping away. As you mop, the water gets dirtier and dirtier, and a certain amount of water is removed from the bucket by the mop and is left on the floor which in turn, concentrates the amount of dirt in the bucket. Additionally, every time you put the mop in the bucket you add more dirt and take away more water.
About half way through the job, the water in the bucket is about half gone and you're having a hard time rinsing the mop, would you simply add more water to the bucket of dirty water or would you dump the dirty water and start again with clean water?
Granted, when you add oil to an oil burner, you are adding fresh oil and fresh additives to the existing oil, but, the oil is already dirty, even more so with an oil burner. Assuming your piston rings are worn to the point oil can slip past them into the combustion chamber, you have to assume that carbon and gasoline is also slipping past the rings and into the crankcase and contaminating the oil which means the oil gets dirtier faster and the additives have to work harder to do their job.
I've always been a strong believer that with an oil burner, if you want it to last, change the oil more often than you would an engine that doesn't burn oil.
If you don't care about the vehicle or are planning on getting rid of it soon, then simply add and drive. If it's a beater car that is on it's last legs, you could even go so far as to add used oil from other vehicles till it either dies or you get rid of it.