CG-wise, you should be able to burn the ballast fuel after take-off, but depending on how you are dispatched, the company may not allow it. But look at the envelope on your weight and balance, and I've never see it exceed the flight CG by burning it. I have seen it go "below" the bottom of the envelope on an IAI converted plane, but that is because IAI just does not show the plane ever being that light.
CWT scavange logic is not armed unless CWT is burned down to a certain level, with 3200kg or below coming to mind. This is why you are told to operate the CWT pumps until the level is 1800kg or less on a normal flight, to then get below the level to trigger the scavange logic. So with ballast fuel, you have not done this, so it will not scavange.
As far as I know, entering the ballast fuel number into the FMC, if that software option is available, only creates the EICAS message for you to turn the CWT pumps off (assuming they were on) at that number, or prevents/inhibits the message on the ground or inflight of telling you to turn them on initially, in the case that you mention, nothing else. The CWT pumps will keep running, etc below the FMC entered number. So if you are using some of the CWT fuel as part of your planned fuel to start with, you need to "pad" the FMC number by a few hundred kg to actually end up having what you want as ballast by the time you get the EICAS msg and react to it, especially during the climbout......
All of the above assumes jet pumps, not the electric scavange pump, but it is probably the same logic.