So I've been looking and haven't found a straight answer.
I'm getting a replacement 3D tomorrow and I'm hoping it doesn't have 1.5 on it so I can root. My question is if I root it with 1.3 or 1.4, can I install the updates and still be rooted?
No, you should not take updates once rooted. You will have issues and possibly loose root. Are you planning to flash a custom rom? If so, then the rom developer updates the rom shortly after an update hits - usually.