Yes you can mow all season and your oil can be so clear you can't see it on the stick if you only mow once a week or four hours a month but if you're mowing everyday and put fifty hours a month on your mower, guess what it's going to turn black. I've used Regular oil and synthetic oil both and it doesn't matter.
At the present time I run a Honda, Kawasaki and two Kohler engines in the business and I use Mobil and have used Mobil 1 synthetic oil both and I change every 25 hrs.
I've also run B&S Onan and Generac engines when I worked for the county and every oil change I have ever done (50hrs with the cheapest crap the county could find) regardless of oil type has always been black as coal so I really don't see where engine type will make a difference.
That's why I said when it's due to be changed depends on how much the mower is being used and the conditions it's being used in, not the color of the oil.