No, not really- negative prices are very short spikes. They aren't driven by fundamental oversupply, they're caused by fossil plants that are unable to ramp down their power output quickly enough to keep the grid in spec. The amount of storage required is very small, but the required power and speed are high.

The whole price advantage of thermal storage is in the amount of stored power. It's very cheap to build insulated tanks. It's expensive to build large turbines, pumps and heaters, the things you need for fast response. Thermal batteries are already kind of iffy compared to batteries (or rather, where batteries will be in 5+ years), so if you skew that price by several factors by going for high power, chemical batteries are definitely cheaper.

In a fully renewable grid, you'd need longer term storage like thermal batteries. 3 days is the most common figure. The electricity price would never go negative, even without batteries- renewables just turn off too quickly. You can just unplug solar panels if they're generating too much power.