Is it bad to have the bottom of a baseboard heater covered?
Baseboard heaters work largely by convection--the heating of air by the radiator fins causes a rising action, and a low pressure zone below. That zone must be replenished. Ideally, open space below allows a "chimney effect" to occur. 

However, since you say that the downstream end of the pipe is room temperature, all available heat is already being extracted, and therefore no efficiency stands to be gained. 

I'd test that, though, to be sure. Take an accurate temperature reading at the downstream end of the system, and if it's more than about ten degrees above ambient you have more heat available to be released with better airflow.

If you can't get the property owner to assist, a small fan directed at the heater would provide adequate airflow to extract additional heat during very cold spells.