Fuel flow rate, as far as I recall, doesn't play into whether OD is engaged or not. More so, it is engine load, TPS position, spark advance and vehicle speed that are mostly determining whether to engage 4th gear or not. Plus then there is the matter of torque convertor lock up and under what conditions that occurs...
If you had insufficient fuel flow, you'd notice an immediate loss of power, like you were towing something too heavy and being weighed down... perhaps misfiring and the engine would struggle to increase in rpm. I've had lots of fuel pumps fail on me in my past -- that's what happens when you routinely run your fuel tank dry - fuel pumps burn out.
