Dr. No, I don't think it's that simple. 2-stroke oils are designed to burn cleanly when they are used in an air-cooled 2-stroke engine which can run a lot hotter than a 4-stroke, especially a liquid-cooled one.
There's also the valves to worry about getting fouled. Big difference between the valves in 2 vs. 4 stroke engines.
Other concerns are the various sensors inside more complicated 4-stroke engines. The sensor may get coated (effectively ruined) by a thin film of oil.
I realize not all of the above apply to simple lawn mower engines, but I thought I'd put all my '2-stroke oil in a 4-stroke' concerns in one post.
Without some serious testing, my caveats remain.