If you run fat tires at quite low pressure, there will be a lot of give, acting a little like suspension. However, if you run the pressure that low, there is increased rolling resistance, requiring more effort to pedal.
So for best performance, you need to run fat tires at a pressure where there is only a small amount of give. As a result there is not a huge range of movement. So they are not really like suspension.
If you ride on a gravel road, for example, or a road with a rough surface, you do get a slightly smoother ride.
Some benefit comes when there may be narrow holes that narrow tires may drop into, but wider fat tires get support from a wider area, and do not drop into narrow holes.