I'm sure that if you drive backwards or stay still long enough in Wii and 7, the game will disconnect you. But what about DS? Never tried and because Nintendo was clueless back then with MKDS being their first Wi-Fi game, there is a chance that you won't get disconnected.
Here are the courses that are possible to do this on. Red font means that assuming the tracks are still limited, you can race on this track in Wi-Fi.
(As an extra note, Rainbow Road and Banshee Boardwalk require you to fall off the track in order to race backwards.)
Figure 8 Circuit
Yoshi Falls
Luigi's Mansion
Desert Hills
Delfino Square
Shroom Ridge
DK Pass
Mario Circuit
Wario Stadium
Peach Gardens
Rainbow Road
Mario Circuit 1
Moo Moo Farm
Peach Circuit
Donut Plains 1
Baby Park
Koopa Beach 2
Choco Mountain
GBA Luigi Circuit
Mushroom Bridge
Choco Island 2
Banshee Boardwalk
Yoshi Circuit
EDIT: I don't think this is possible on Tick Tock Clock or Frappe Snowland. Removed both.
Here are the courses that are possible to do this on. Red font means that assuming the tracks are still limited, you can race on this track in Wi-Fi.
(As an extra note, Rainbow Road and Banshee Boardwalk require you to fall off the track in order to race backwards.)
Figure 8 Circuit
Yoshi Falls
Luigi's Mansion
Desert Hills
Delfino Square
Shroom Ridge
DK Pass
Mario Circuit
Wario Stadium
Peach Gardens
Rainbow Road
Mario Circuit 1
Moo Moo Farm
Peach Circuit
Donut Plains 1
Baby Park
Koopa Beach 2
Choco Mountain
GBA Luigi Circuit
Mushroom Bridge
Choco Island 2
Banshee Boardwalk
Yoshi Circuit
EDIT: I don't think this is possible on Tick Tock Clock or Frappe Snowland. Removed both.