Unlikely after trying to power it on several times since it happened, as the juice is a salt that corrodes (and shorts out) sensitive internals. However if you really want to try, go find some 99% isopropyl alcohol (it CAN be found at drug stores, but might take a couple of stops, not much is kept in stock). If you can't find it, 90% will do, just has to dry longer and more likely to get water spots.
Pull the batteries and/or any power to the device until this is all done. Dunk the DS in the alcohol (if it doesn't work, won't matter either way since it's dead). Let it soak a long while, turning if you see bubbles stop, until you get more bubbles from any seams/ports to stop coming out. After soaking awhile, take it out, drain/shake it out very well, then dunk it again. Repeat several times, the idea is for the alcohol to dissolve any juice residue and related salts and drain them out. After 5 or 6 repeats of this, shake it out as best as you can, and let dry for a day or two (or on the floorboard (not dashboard or direct sun, it can warp/melt) of your car in the sun). Or get an electronics "dry bag" (designed for this purpose) to help dehydrate/dry out the DS. I'd still wait at least 2 days for good drying, shaking periodically to move around any wet alcohol spots internally. Once you are sure it's dry, then reinstall power and try it out. If it worked, it'll work, if not, it'll probably be doing the same thing it was before. Or it might do something else, but still not work, as things may have changed from the juice internally.