I have a friend who works in matcha stores, and he claims that he prefers N2O over N2 because it has a "sweeter flavor." Further, N2O is what's commonly used, I believe, in iSi whippers to make whipped cream or, if you're Dave Arnold, pressure-infuse tinctures, so its use is not limited to the dentist.
Chemically, and take this with a small-ish grain of salt, because N2O is polar, as some above have noted, you'd expect it to dissolve more readily in water, and hence beer. NIST has CO2 and N2O as having Henry's Law Constants of .034 and .024 at 298K in water respectively, with N2 at a distant .0006, which backs this up.
As such, you'd probably expect it to escape solution more slowly (as CO2 does vs N2), for whatever that's worth - it might even require a low psi, as CO2 does vs N2 for 100% "carbonations" of each gas.
As to the question of oxidizing, I don't see why it would oxidize your beer any more than CO2 - the question is one of molecular stability, though without knowing more, suffice it to say, perhaps N2O is highly unstable (although I doubt to that degree, or much more than CO2, say). H20, for example, contains oxygen, and in a solution as big as a pint, I guarantee you the occasional oxygen molecule is spontaneously produced by collisions, or hell, fusion, but we don't worry about such small concentrations, as they're truly insignificant.
Another point: it's not illegal to use this commercially for beverage purposes, as you might expect given its psychoactive properties - the matcha friend showed me
this, which I suspect is legitimate.
Finally, as to the ability to use this gas to serve stouts, one could easily use one of the "mini" regulators that takes, say, iSi whipper-style cartridges as gas sources, and use a N2O capsule to dispense, even "carbonate," beer (assuming the fitting is the same, which I think is fair - hell, you could carbonate and serve from an iSi whipper if you really wanted to!) - which is to say, the friend was potentially not confused at all
So, to bring this all around, the use of N2O in force "carbonation" seems not just plausible, but potentially interesting given the flavor profile of the gas, use in adjacent industries, and, I theorize, more "sturdy" dissolution in beer - let's just hope Brulosophy picks this experiment up soon!