In a word, no.
Why does oil turn black?
Soot particles are tiny (<1 micron), and they darken the oil. Oil turning black depends on so many factors - fuel quality, combustion quality, usage patterns, engine condition, care taken in the last service and more.
If your fuel is lower in grade, combustion is less complete. More expensive fuels also contain additional lubricants and cleaners which may reduce the amount of soot in the oil.
If you have poor ignition components, your oil will turn black quicker. Worn or incorrectly gapped spark plugs will have poor combustion and lead to black oil.
Heat cycles also cause oil to turn black. If a car does lots of town journeys, it doesn't get up to operating temperature so the tolerances may lead to more soot getting into the oil.
This is the factor you're worried about - worn piston rings for example. While this is definitely a factor, there are other ways to figure out how worn an engine is - oil consumption, fuel consumption etc. are better measures. Check your oil and fuel consumption are within manufacturer limits.
Care in servicing
This isn't to do with engine servicing - I'm assuming the engines are serviced according to manufacturer recommendations. There is a huge difference between "suction" removal of the oil and replacing it (jiffy lube etc. - cheap and quick services), and a proper drain and refill service. The drain and refill will get much more of the black oil out, so the new oil will be cleaner for longer.
Personally, I remove as much of the oil as possible (drain oil, pour a little fresh oil through the top and letting it drain, and remove as much as I can get from filter housings etc. using suction at the end before putting it back together and refilling). This care probably means I'm replacing 80-90% of the oil, compared to as little as 50% for the suction/refill method. It takes time, care and attention to do this though.
All these factors together mean that it's difficult to attribute oil blackening reliably to any one of these, without being methodical and scientific about how you're measuring and what variables you're changing.