Yes, absolutely don't try to tow without trailer brakes and a controller operative.
Besides power and ground, the controller needs a 12v input signal which is active only when the brake pedal is depressed (and the brake lights are on). The signal draws very little current. This signal is usually taken either straight from the brake pedal switch itself or from the 12v wire to the brake lights. The 12v power to the brake lights is also used, usually via a device called a "taillight converter" or "adapter" or "modulite", to light the trailer's brake lights. So if that is possible, then I don't understand why that signal can't be used for the brake controller. In the very worst case, you or the hitch installer should be able to install a second brake pedal switch which, with one side connected to 12v, provides the brake controller with the signal in question. This will probably mean fashioning a custom bracket to hold the switch in the right place, though.
As far as using the RX to tow the 2720SL, search this forum's towing rigs section. You will find those who say they tow just fine with the Rx, highlander and similar shortish-wheelbase, 3500 lb towing spec vehicles (WITH trailer brakes, that is - the spec is much lower without them), especially if the terrain stays flat. You will find others who will say they consider such vehicles inadequate.
-Paul
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