No. Race ties you to a vehicle at all times. The only thing you can do is alter the amount of time someone can be off of a vehicle before teleporting back.
I couldn't find the option to change the amount of time someone is off a vehicle before they are forced back onto one. Can you elaborate on how I can find this option? Also, is this a feasible means of making checkpoints? I would use teleporters but there are not enough.
I guess you could do this kind of thing with Invasion Phasing... Unless it has to be Free-For-All and you have to actually race to each checkpoint. I'm not sure if you're just using it as a means of respawning or not though.
I will be using these checkpoints for an obstacle course. I want each person to earn their way through the course and not backpack off someone's hard work.