Can a device use more wattage than it's rated for?
The voltage is constant. Whatever your outlet supplies. (Yeah, fluctuations in that do happen, so that could be a factor.) Under normal operation, the power consumption is determined by the current being drawn, which can change during operation. A cold electric heater will draw more power than a hot one, because hot coil has higher resistance. A motor will draw less power once it spins up to maximum speed. And so on.
But yes, power rating is the design maximum. It's what device shouldn't be exceeding under normal operations. If nothing goes wrong. In general, it's a little more complicated than simply having fixed resistors. There is more stuff going on depending on what it is that the device does. But overall, your statement is closer to the truth. If nothing is wrong, device will not draw more. It can certainly draw less.