Well, I'm not Blackstone, and not a Tribologist, but I would say it would be wise to change the oil. You have condensate, plus products of combustion in the oil, and some of it is emulsified(will never separate until it is boiled out).
Oil is cheap, engines are not. I will offer an opinion that synthetic oil is not used in air cooled small utility engines. We do not have pressure lubrication, and rely on some amount of surface tension and stickiness so I prefer straight weight dino oil, but this may set off a lot of controversy.
I know for a fact that aircraft with air cooled engines did not react well when Mobil introduced a full syn oil for Lycoming and Continental air cooled aviation engines. In fact, Mobil was the source of several engine failures in flight, causing a few deaths, and planes destroyed. Mobil was forced to remove the oil from the market, paid out some large claims for damage, and is now very cautious about anything aviation. Our air cooled engines also use oil to help cool, and the dino, non-syn oil is better at heat transfer than modern syn oils.
YMMV
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