how upright does an OB need to be to drain cooling water ?

Will only drain out fully when vertical, if tilted there will be some water in the bottom of the gearbox where the prop shaft carrier meets the bottom of the exhaust downpipe.
 
Likely find that they have drained and expelled any water before being tilted to an up position. Not to say that they won’t have rain water sitting in the exhaust cavity though. I always tilt mine down after she comes out for storage then lift a little afterwards in case the yard need to move the boat around over winter. Put a prop bag and full cover on it additionally too. Do the same with my outdrive boat too.
 
They don’t drain straight away, you have an impellor above which is a pipe going up to the engine block. Thewater fills up the block and when it gets to the top it then overflows into the exhaust manifold cooling jacket and the free falls out of the leg. When you turn the engine off this drains down but the water in the pipe above the pump slowly leaks out past the impellor, some drain quicker than others.
 
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