He can when your opponent is at low damage, however its MUCH easier to do it on a computer than a human. Also, its much harder and sometimes not possible against some lighter characters.
Most of the time, if your opponent knows how to DI out of it, you'll only be able to connect 2 throws. It works best when you catch your opponent off-guard.
These are some good chain-grab combos to keep in mind:
1) D-throw > D-throw > Dash attack > U-tilt
2) D-throw > D-throw > Mach Tornado/F-air/D-air
3) D-throw > U-throw > Shuttle Loop
4) F-throw > F-throw > Mach tornado/F-air (against heavy characters)
Hope this helps
EDIT: MK doesn't have any true chaingrabs. Sorry, I use the term chaingrab loosely.