Example, your 3DS is connected to your home's wifi. If you block your 3DS from wifi, will you still be able to see that blue Internet bar on your 3DS?

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Author of the Ruby Destiny series~

If your 3DS's wifi switch isn't turned on. The bar will still be there, but it'll be gray and says "Disconnected" or something like that. But if the wifi switch is on, but the home wifi is off or if your 3DS is out of range, the 3DS goes into Streetpass mode. Where the bar is colored green and says "Streetpass".

Thank you, but my question revolved around if your 3DS is blocked from accessing wifi connection.

__________________
Author of the Ruby Destiny series~