Blocking the EGR won't do it, but a fault in the EGR pipe would. So would a leaking exhaust manifold or any of the joins in the exhaust of which there are a few:
cylinder head -> exhaust manifold
exhaust manifold -> turbocharger
turbocharger -> dump pipe
dump pipe -> catalytic converter
catalytic converter -> exhaust pipe section
If DPF fitted: exhaust pipe -> DPF and DPF -> more exhaust
more exhaust -> muffler (which is NOT at the rear of the car)
muffler -> last pipe section
The trick is to look for sooty black powder emissions. I'd concentrate around the exhaust->turbo and EGR areas, they're quite prone to faults.