Can you use a 3DS cartridge on a different console despite there being extra data saved on the console it was originally played on?

[Frenetar]

Let's say Mario Kart 7 for example, where spotpass and streetpass was used. Would that corrupt the cartridge?

 

[hippy dave]

No, the cartridge will work fine, but obv won't have access to whatever data was on the other console.

 

[CoolMe]

Let's say Mario Kart 7 for example, where spotpass and streetpass was used. Would that corrupt the cartridge?

Nope. It should work fine in any other 3DS you plug the cartridge into, regardless of the extdata. Not for stock out-of-region 3DS's though..
If your system has cfw installed, you can backup extdata with Checkpoint, and restore it in the other 3ds that you wish to play the cartridge on.