There's a section of a local highway that has water grooves parallel to the direction of travel. When driving the highway in my 2012 Prius Three it feels like old bias ply tires. The car tends to oscillate slightly sideways. I driven that same section of highway many times in my Highlander without that effect. Is this a function of the low resistance tires?
More so a side effect of the specific LRR tire you are running. The Yokohama S33D has this problem. The Energy Saver A/S does a tiny bit as does the Yokohama Ascend. I think a lot of 15" tires on this car are like that. Going to a 17" tire cures most of it.
So I guess the answer is "yes". Of course they aren't bias ply tires but they have a similar effect with some road conditions. Its amazing... so many design features added up to give good mileage.
I think you're encountering Tire Tech Information - Tramlining: Coping with the Ruts in the Road. I don't think I've ever driven a car that didn't have radial tires, so I can't relate to any bias tires.
Some folks put bias ply tires on their classic cars to be correct for the year. I have radial tires on my 1949 Ford.