The condition which cause the mass change is very important, and can not be ignored in general.
Because when you add mass to a system, you are some interaction occured. (for example: it could be in-elastic collision or collision occurs)
And the dynamic of the system is determined by the external force (i.e. the way interaction occurs).

I will assume the momentum and angular momentum will be conserved, but energy is not conserved for most of the case (unless only elastic collision occurs).
So if the mass was added to the system and the process did not increase momentum to the system, then the velocity and angular velocity will become smaller.
However, if the momentum was also increase, then it is a different story.

There are too many possible outcome become you did not specify any condition.
If we really want to discuss a problem, we should make the problem clear.
It will be easier if it is a well defined problem.