He and his administration probably does in fact believe that, but I still lean toward thinking that they're being played. I don't think that Russia will do anything that will result in most NATO countries saying, "Yep, that was definitely an invasion of Ukraine, so now we're doing all of the crushing sanctions we'd planned." If Russia fully withdraws without much incident like they've been publicly saying, then at this point it'd be a big blow to the credibility of Biden/America/NATO. Even more likely is that they continue their threatening posture to keep the West in an uncomfortable state of limbo for months.
I wouldn't bet much against an invasion, though, and on the other side of the argument, if Putin knows that he eventually wants to take a piece of Ukraine, now would be the perfect time. The energy market is currently uniquely favorable to Russia, German politics biases them strongly against cutting all ties with Russia, Putin needs a boost in his domestic approval, etc. Also, if Trump is president in 3 years (a distinct possibility), then an attack against Ukraine years in the past under Biden isn't something that Trump would particularly care about.
It looks like if they will do something, we're most likely to see it in the next few days.