Yes, CarePenguin will work with tankless water heaters. CarePenguin works by measuring the temperature of the hot water heater output pipe so both tank-based and tankless water heaters work with CarePenguin.
One thing to know however, is that some higher end models of tankless systems include hot water recirculation systems built in. If this feature is present and activated, then the tankless unit automatically heats water in the hot water lines in the house all the time. This is incompatible with CarePenguin.
You will know this is the case if the analysis graph in the app shows the usage pattern on the left rather than the usage pattern similar to that on the right.