What if you don't use 2 cycle oil in a 2 cycle oil motor?

As your engine system is a "total loss" lubrication system, where oil is either added direct to the fuel in the tank or introduced via a valve to the inlet side of the carbs from a separate oil tank. In a two stroke engine the crank case of the engine is used as a transfer chamber to introduce fuel/air/oil mix into the cylinders and it cannot hold upper cylinder lubricant. Thus the engine depends upon (2 stroke) oil dissolved in or delivered with the fuel air mix for both upper cylinder lubrication and cooling. Without the oil, the engine will rapidly overheat and the piston rings will expand into the cylinder wall and "seize" the engine, causing scoring to the bores. There is also the risk of further damage to the bottom end (main bearings) where they interface with the crankshaft. All in all - not a good idea to run a two stroke without the recommended oil in either the premix pump or added to the fuel.