Hello there! Yes it is possible, but it would be a good idea to check a couple things. What was the smell you noticed?
If there is an oil leak somewhere leaking on the exhaust, this will give you the smell youre describing. Start by looking under the car for oil drips down on the oil pan. Gravity pulls any fluid leak down the engine, while the force of air while youre driving and the cooling fans blow the fluids towards the rear of the car. If you see a black stain on the exhaust pipe or floor boards, look up to see if you can locate the source. With an engine getting that old, (16 yrs), its common for the valve cover gasket and other seals to fail. If the oil level is low, this would explain the oil light coming on. If the oil grade is too heavy (10W30 or heavier) oil will not circulate properly till it warms up. If the engine is running at a high RPM, the oil may not run back down to the oil pan for re circulation buy the oil pump, the oil pressure will drop turning the light on.
I looked under the hood and there are no oil around the seals, none on the ground-it doesn't appear to be leaking, and the amount of oil was spot on???