Possible, doable on any user hardware, doable on readily available user hardware and doable on proper custom hardware is but a fraction of the potential spectrum here.
I have yet to see any analysis of the 3ds for want of a better term nifi so I will have to look at similar projects.
Networks come in layers and I do not especially care to go too much further there right now (a search for network layers will get you enough to bore you silly for the next three weeks though I guess I do encourage knowing what the OSI model is about and what it is good for).
If it was just a matter of transferring conventional network communications then it would probably have already happened as we have VPN for a reason, I will note that there are ways to gimp this (either at protocol level or artificially) as indeed the 360 did for receiving consoles in "system link" titles (why you need low latency aka pretty much only LAN or a JTAG/RGH hacked box for everything other than the host).
The DS would probably then be the place to look now. This is where I come back to layers and variations on the theme- network communications are highly standardised and this often plays out right down to the hardware level (if it is all going to be standard then you can make your hardware do a lot of the work for you). There are tools to break from this and allow raw or otherwise nonstandard transmissions and decodings- if you wanted to hack WEP security this is usually why you are directed at certain makes of wifi card (though there are a few deeper reasons like open source drivers and other reasons for that).
It goes a bit further though and what counts as raw for the purposes of conventional network hacking methods (we already did wifi but see also raw sockets) and what would be required here (if you really want to a bit more technical Cyan has you covered-
http://gbatemp.net/threads/xlink-kai.334836/#post-4398938 ) might not be quite the same.
Again it might not be the case on the 3ds but I would not be surprised in the slightest if it was the case here.
Coming back around though the 3ds having more security and a proper kernel (thinking the 3ds might look something like a wii in terms of architecture) might change things here depending upon how it is all set up where on the DS it was going to be custom/rare hardware and a lot of fiddling or not at all.
