If the actual balance shaft if funked up as your mechanic is saying then it stands to reason that the oil pump might have suffered damage or perhaps the block internally too.
Your gonna need to check with your mechanic to find out how he has determined what he has told you and maybe post a pic of the actual shaft up on here too pal. If he's got it out.
Is the mechanic proposing to remove the pump and inspect (if so, delete it) or is he planning to just refit another balancer shaft as is?
Sounds a little iffy to me.