It’s possible an EGR fault could cause this problem but my feeling is that the hesitation is due to something else. It might also depend on exactly what EGR code is present as there are a number of them.
A hesistation could be caused by a general state of tune problem, vacuum leak (EGR is a vacuum leak of sorts), TPS switch problem, MAF sensor, etc, etc. This could also be caused by a transmission fault based on the comment about slow speed and high RPMs.
The EGR is an emissions device that controls NOX and is not something you would physically notice. The EGR also controls combustion chamber temperatures and this is critical. If you hear a rattle on acceleration that sounds like a rock in a can then the EGR is probably the cause of this. If it’s bad enough and left unattended it can be engine damaging. If there is no rattle on hard acceleration when the engine is fully warmed up then odds are it’s working ok.