...my guess is that the nitrogen would be easily taken up by plants.
Hi, great idea, but I don't think it will work. Here's why...
I quote directly from Wikipedia, a few sentences here and there, put together explain it well...
"Nitrogen fixation is a process by which nitrogen in the Earth's atmosphere is converted into ammonia (NH3) or other molecules available to living organisms. Atmospheric nitrogen or molecular dinitrogen (N2) is relatively inert: it does not easily react with other chemicals to form new compounds. The fixation process frees nitrogen atoms from their triply bonded diatomic form, N≡N, to be used in other ways."
"Microorganisms that can fix nitrogen are prokaryotes (both bacteria and archaea, distributed throughout their respective domains) called diazotrophs."
That being said, atmospheric nitrogen and nitrous oxide are not the same compound and nitrogen fixation occurs with diatomic nitrogen, not nitrous oxide. Now, there is nitrous dioxide fixation, but it is something seen mostly by extremophiles, that's bacteria (prokaryote/archaea) that live in nearly boiling water at underwater marine volcanic vents, it's not anything relevant to keeping a planted tank. See:
Biological N2O Fixation in the Eastern South Pacific Ocean and Marine Cyanobacterial Cultures
Also, keep in mind that something like 70% of our atmosphere is nitrogen already, which you would be aerating in an aquarium for the 16ish% oxygen content.
I would be very surprised if adding nitrous oxide to your tank would have any effect at all for the plants. I'd be more worried of the effects it could have on your animals.
I'm not discouraging you from trying something new, I just don't see it working as you might have planned out. If you do decide to try it, I would be interested in your updates and methods.