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Unfortunately not. The wi-fi service for DS games (not 3DS fyi) was discontinued as of May 2014, so the only way you'll be able to trade in B/W and B2/W2 is via local wireless, meaning you'll need either another player nearby or a second system.
With that said though please do hang around this forum either way and chat with everyone about your playthrough! We may not have wifi capabilities but we do have lots of fun here ;)