I don't think you will be happy with the handling of your Sprinter with a 500 lb motorcycle plus 150 lb carrier (you will need a really sturdy carrier to haul that heavy of a bike) on your hitch. A trailer is a much better solution for that much weight. That 650 lbs is going to feel more like 800-900 lbs because of how the weight is centered 2 feet behind the hitch rather than right on top of it like trailer tongue weight would be.
We haul two motorcycles behind our Ford Transit (both are Yamaha WR250R dualsports, so under 300 lbs each), but do so in a 5x8 enclosed trailer. There are a lot of advantages to using a trailer. We use Pitbull Trailer Restraints, so we can load/unload the bikes in minutes. The trailer gives us extra space for hauling our riding gear, tools and gas cans. And it is a convenient place to change into riding gear once the bikes are unloaded.
The trailer tucks in very nicely behind the van, since it has a lower roof line, and the 5' box width is narrower than the van. The axle width is about the same as the van, so it tracks really well. We give up about 1.5-2 MPG when towing (less in the flats, more in the mountains). Total loaded trailer weight is about 2000 lbs, and tongue weight is about 250 lbs.
Motorcycle Carrier Recomendations
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