Alphotodoc and Larry -
I am under the impression that some of the Swagman racks are simply a sleeve that fits over the stem or shank of the hitch. This type doesn't "extend" either the receiver or the hitch.
See, for example
http://www.prolineracks.com/Swagman-...wing-rack.html
It would seem to me that this last type does have an effect on turning radius - how much, I can't tell you.
You might also consider an Allen rack such as the 143 or 103 (which I use). MUCH less expensive than a Swagman. Of course, the Allen rack also has an effect on turn radius.
http://www.allenracks.com/products/trunk/143a.html
Some Swagman racks are rigid, which means you have to remove the rack from the hitch (which means remove the hitch from the receiver) if you want to open the tailgate. If your trailer is already on the hitch, this is a real pain. On the other hand, some Swagman racks (such as the one in the link above) can be folded to allow access to the tailgate.
The Allen rack is not connected to the hitch, so it can be removed at any time, although you need to take the bikes off the rack first.
You can do an Advanced Search of this site for "Allen" or "Swagman" or "bike rack" and learn a lot from previous discussions.
Bill