Please fill out your signature and tell us what year of truck you have. This will help the members to inform you better on what to do. The newer trucks, say from 2013.5 and up that use DEF have less EGR taking place than the older diesel trucks say from 2007.5 and up to 2012. In fact the newer trucks do not even require the owner to service the EGR cooler anymore since the exhaust gasses use has been cut back. The 2007.5 to 2012 still require the EGR cooler to be service every 67,000 miles or so.
Yes; you can unplug the EGR but you can not remove the crossover tube. You will get a CEL but the truck should operate with no issues. I did this to my 2008 and ran this way for a year until I decide to allow the truck to go under the knife for surgery. The engine will put out exhaust gasses to the turbo and still will dump them into the intake air system but at a slower pace. But you do not really need to do this with the newer trucks from 2013.5 and up since as mention above less EGR is taking place.