Can an OpAmp work shortcircuited to ground?
Generally they are not designed to withstand a continuous short circuit to ground, so you'll negatively affect the long-term reliability, at best. 

Exacerbating factors- ambient above 25°C, high supply voltage, more than one amplifier in a package shorted, more than momentary duration (thermal and electromigration failures can occur). 

Even where "short circuit protection" is claimed, there are usually weasel words in the datasheet such as 


  temperature and supply voltages must be limited to ensure that the dissipation rating is not exceeded


(TI TL071 datasheet). Since there is insufficient information to calculate the limits, they're really telling you that it's not something you should depend on. 

The "short circuit" protection can usually be depended on for brief high current surges occasionally and for protection against sloppy probing on a PCB in a lab environment, but for anything else you're on your own and good luck.