Asked straight up most people's response would be "no, stupid", especially since it doesn't have java or flash. Where you or I would see that as an impediment, however, the folks behind Project Triniate see it as a challenge.
While crude, it appears they've got the basics up and running, and while you may never get to play it yourself, it looks like the project's site is already there and ready for a 3DS browser.
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Nobody said it was going to be awesome. Just that it was a challenge to be overcome!
A browser-based MMORPG for the 3DS [Nintendo 3DS Blog, via Go Nintendo]