As far as performance, you won't know it's there. We tow with a gasser and have to use the rear camera to know it's there, so with a diesel you should be even better.
As far as mileage, I find it really hard to compare towing and not towing because there are too many other variables like wind direction and speed and terrain. You can't pull 3500-4000 lbs without some effect, but to me it's not significant.
Doug & Sandy
Kaylee (8 year old Terrier of some sort), Kaiya (6 yr old Golden)
Jill & Henry at the Rainbow Bridge
2009 Honda CRV
I also have a 300 HP Cummins, but it is an older (1993) mechanical 8.3 and my coach weighs 26K loaded. We pull a Hummer, which weighs more than your CRV, but previously pulled a Mustang convertible which probably weighs about the same as a CRV. We rarely notice the toad except on steep climbs or steep down grades. Our fuel consumption is about 1/2 of a mpg between towing and not towing.
Holiday Rambler Navigator DP, Hummer, and Honda VT1100C Shadow