In terms of impact on range, it's hard for me to say for sure, because I've never taken the X on that route before, and there were a lot of variables that likely also played into my range during the trip: temperatures of 100º-110º on the drive through the desert, heavy side-to-side wind, etc. I did need to charge at each stop for about 25 minutes, and the total trip distance was about 250 mi. I arrived in Laughlin with about 30 miles of range left.
The carrier had no impact on how it felt to drive the X, you couldn't feel it back there, except when backing up (rear camera view blocked of course).
On the trip out, I let the X automatically put me into full trailer mode, which disables Autopilot, and only radar-assisted cruise control is operational. On the way back I decided to manually turn off trailer mode to allow for Autopilot, but I disabled automatic lane changing, as I deemed that was the only real Autopilot-related risk with a longer tail and impeded rear sensors. Used AP for most of the trip back with no issues at all (manual lane changes).
Since the X still detected that something was connected to it electronically, it still shows the trailer dash light, but in orange instead of blue, to let you know that trailer mode is technically off, though the blinkers/brake lights should still function.