On occasion if a departure SID has 'At or Below' altitude restrictions at different waypoints we would select the most restricting altitude in the MCP initially before departure and ensure that the FMS was programmed appropriately for a backup to ensure no level busts. The low level off is selected in the MCP because often its so low that we would reach it before flap retraction is complete and in my aircraft we do not select a FMS controlled climb (VNAV) until NADP is complete.
I usually only encounter this in the Canaries and if a controller clears us to a higher FL than the SID restrictions I would select the cleared FL on the MCP (so the Mode S downlink indicates we've selected the cleared FL), and leave the crossing restrictions in the FMS unless the controller gives us an unrestricted climb. As far as I know the FMS restrictions are not downlinked via ModeS/ADS.
We would never select a higher FL than cleared in the MCP.