When the factory puts the engines together they are done with a certain amount of plus or minus tolerences. For general service they will vibrate a certain amount, but generally not enough to concern the general public. This also allows the replacement of flywheels, balancers, pistons, rods and crankshafts in the field with off the shelf parts and still having and engine that will not shake itself apart. When an engine is balanced at a machine shop, everything is made the same and balanced to work together.
The process involves taking the lightest rod and grinding material off the rest to match the weight and the same with the pistons. The crank is then matched to the piston/rod assemblies and finally the flywheel and balancer are matched to that.
Unless an extreme amount of weight was removed from the rotating assembly, a replacement balancer or flywheel, it will likely still be within the tolerence enough not to shake itself to pieces, but it will likely not be as smoothly balanced as it was when it came back from the machine shop.
Most shops that do balancing provide you with a "Balance sheet" which provides you with the weights of the rotating assemblies. If you have this, they can rebalance individual replacement peices to match the rest of the engine, without taking the engine apart and rebalancing everything.
If you don't have this, they may be able to use the flexplate and balancer you currently have and balance the new parts to match.
Well, a little long winded, but hope this helps.