Can I use the 'add a new battery' feature to add a supercapacitor instead?

If you want to model a large supercapacitor that functions as an energy storage device, meaning the system can use it to store energy from one time step to the next or from one day to another, you can do that using HOMER's battery module.  I would expect a supercapacitor to have a flat capacity curve, a really high lifetime throughput, and a high round-trip efficiency.

On the other hand, if the supercapacitor does not store much energy (e.g. only enough to serve the load for a few seconds) and it primarily affects power quality or system stability, HOMER cannot model that because it does not model those effects.