This Erowid contributor gives anecdotal evidence of his own addiction to the stuff. But Erowid makes it look like the biggest dangers from the stuff come from suffocation, frostbite, or injuries resulting from trying to walk around on the stuff. It’s cagey on the subject of addiction.
As for myself, I’ve been using the stuff for years. About once or twice per year I’ll buy a box of cartridges and spend the next few hours buzzed. But after it’s gone I forget about it, and I don’t jones for it.
I say no, the one or two times I’ve done it I thought it was awesome, but once I pulled the mask or whatever off, the buzz ended instantaneously and I wasn’t jonesing for it afterwards.
There are case reports of hospitalizations involving complications from severe vitamin B12 depletions in patients who were inhaling a dozen or more cartridges of nitrous oxide every day for a couple of months.
You realize that the above doesn’t answer anything. By your reasoning, all drugs are addictive. But even the US government doesn’t label all drugs as addictive, e.g. LSD : “LSD is not considered an addictive drug since it does not produce compulsive drug-seeking behavior, as do cocaine, amphetamine, heroin, alcohol, and nicotine.”. This despite the fact that there are a few people who use LSD very extensively. So, the “some do, some don’t” characterization is vacuous. What’s usually implied by the shorthand of “is this drug addictive?” is “is addiction to this drug common?”. For nitrous, that answer is probably No. Even for cocaine, addiction is a minority outcome, like alcohol.
A more interesting question is whether it is physically addictive, even though physical addiction is easier to treat than psychological dependance. (That is, it is amenable to detox, which is a fairly standard procedure, as opposed to requiring an unknown amount of psychological therapy.)