I lost my tee time due to a frost delay at Balboa this morning (again?!?!), so I went to the range later in the morning. I was practicing putting, and happened to grab a couple of the Srixon Divide two-tone balls. I found it really helpful to line up the ball, and see the roll out with the orange half on one side, and the yellow half on the other. I found that much easier to see than just a line on the golf ball.
So can you play with one ball, and putt with another? As it turns out, no.
For high-level tournaments, they often have the one ball rule in effect. You can only play the specific model of ball that you start the round with. That's only at the highest levels, though. For regular SCGA play, you can swap in a different ball at the start of a hole, or any time you are taking relief. But you cannot swap in a ball to putt with unless the ball you were using is cut, or otherwise damaged.
It could be advantageous to use a specific type of ball for a specific hole, given certain wind conditions, or the like. But it has to be a conforming ball, so it's probably not going to be much of an advantage. And as noted above, you can't do that at the highest levels of the sport.
