The answer to this is, unfortunately, both yes and no.
The heatsink-fan unit is indeed removable. There are two components that are connected to the heatsink, one in direct contact with only TIM (Thermal Interface Material - paste) between them and one in contact via a thermal pad (because of component height differences). In placing the board into a fan-less chassis, both of these components need to be properly in contact with the heatsink - usually via a replacement pad (though, if chassis' block is milled to handle the height differences, a solution with only TIM may be possible).
OK, that was easy part. The problem is that the heatsink-fan unit is also providing the airflow that is cooling the components on the opposite side of the motherboard. When the fan (blower) pushes air out of the chassis, cooler air is being drawn into the chassis on the opposite side of the motherboard and flows over and around the motherboard (thereby dissipating the heat on the that side) to get to the opposite side. If you go into a fan-less chassis, you need to make sure that you are not creating a problem on the other side of the board as a result of no airflow. In the case of an M.2 SSD, this likely requires that it also be in contact with the chassis exterior (usually via a thermal pad).
There are companies that have analyzed the situation on these motherboards and have produced board-specific custom (fan-less) chassis that are designed to handle all of these issues. If you are purchasing one of them, great. If you are trying to do this from scratch, however, you need to take all of these thermal issues into account...
Clear as mud?