Sort of.No, which is why the solution is bigger tanks
Total water output can't exceed production over a long time span. A large hot tank gives increased instant capacity; however, a large depleted tank also takes a long time to recover (temperature wise).
That's why series connected/ cascade water heaters are handy, they combine their heat output and provide surge capacity along with improved near term recovery.
Heat pump heaters are going to be slower. Just due to the design choices they have made towards efficiency.
For normal single unit sized setups. Gas is higher BTU than electric, and heat pump is lower BTU than electric.
Rheem has 4,500 W backup element which is 15k BTU. Heat pump is 4.2k BTU/hr.
For reference, if incoming water is 60F and hot is 120F, 1k BTU/hr provides just over 2 gallons per hour.
One could stack three 40 gallon units in series and get >150 gallons first hour and 25 gallons an hour recovery using the heat pump only or 80 gallons HP+element (extra 15kW).
Roof solar water heaters and heat recovery from dryer and waste water would go a long way towards reducing energy needs (but adds complexity).
Roof solar to large holding tank(s) with indirect heat exchanger might be interesting .