In addition to what others have said, I'm thinking that even if they allowed you to wait for two spots to be available (and for there to be no groups of two toward the front of standby/FP lines), it's really hard to say how long you would have to wait, and it may well cancel out the benefit of the single rider line. And you'll be split up during the wait if one parent takes a single open seat and the other parent waits for two seats. It doesn't sound practical to me, even if it was allowed. Also, it may depend on the CM, but I believe there are some rides where you have to be seated next to the 6yo, not just in the same ride vehicle (I saw a dad and 6yo twins taken off Screamin' because there was no way the dad could sit next to both kids), so on those rides you would potentially have an even longer wait. If I were you I would just try to make good use of FP and use single rider for anything your kid doesn't want to ride.
But if you want to try it, you can always ask at the front of the line and see what happens.