hahaha, but No
I have one of these card and I was fortunate enough to buy one a couple weeks after it was released, which was about a year ago.
The GTX 1080ti by it's self draws around 250w and that's not including any kind of Boost clocking or overclocks. Some of these higher end GTX 1080ti cards on the market like the Asus Strix model will consume 285w. This figuring is just the card alone, which doesn't account for the rest of the system. You're probably looking at another 100w for the rest of the system if not more.
That might push it close to 400w while gaming but there are other factors to look at here. For one, it's always recommend to not push a PC power supply much past 80% of it's capacity. Any quality power supply reaches it's peak efficiency at around 25% usage, but the efficiency starts dropping off at 75% capacity then at 90% capacity it takes a significant hit. When you figure this in, 650 is a good number, which is what is recommend by Nvidia.
As a general rule of thumb, if your power supply doesn't have the right connection ports and plugs for your Graphics card then it's time to buy a new power supply. There is a reason a 450w or some of these 550w power supply units don't come with the right PCI-E power connectors for a high end card like the GTX 1080ti.