Maybe Yes, Maybe No is the immediate answer to this basis question as of course it all depends on the inverter you currently have.
First you need to understand that straight forward grid tied inverters are generally not compatible with batteries and you need what is known as a hybrid inverter
Basic inverters are only designed to convert the DC power your PV array generates into the AC power grid connection your home uses.
As batteries also store power in DC format you need an inverter that can manage the flow and conversion of energy between 3 different sources ie Grid/Home (AC); PV array (DC) & Batteries DC.
This is a complex process especially you take into account how and when you generate/consume power.
Having a system that learns from the patterns that emerge of your consumption / generation usage is just as crucial as the battery itself.