While running you most likely wont notice a regen since the engine is hot and at higher rpm. When at idle you will notice a regen as it should automatically kick the RPMs up, a few hundred to build heat.
On my heavy equipment, sales people have told me its ok to shutdown during a regen if it has the ability to restart on the next trip automatically. However, the mechanics on the service side have told me to just let it perform the regen and advise not shutting it down since it has to reach temp to restart regen. If you shutdown and the next trip is too short then it never starts back up to finish the regen and waits till the next trip or time that conditions allow it to restart. Personally on all my equipment if it is in a regen we let it finish and keep it running, it usually is 20-30 minutes so not too bad, but if we pause it it seems to be a longer process. This is all based on my experience with my equipment, maybe the 6.7 is different.