RTA cabinets are like already assembled cabinets, in the sense that they vary in quality and price.
The price savings come from the fact that the are not assembled and they are easier to ship.
I think with a little comparison shopping they can be a good alternative.
Removing the door and properly flashing and sealing it is the number one solution.
If that is not an option you are willing to consider then about the only thing you can try is to caulk it from the exterior.
Just remember caulk should never be your primary water control measure.