The short answer is yes. People have been running 240V inverters from AGM batteries long before lithium was around. But people have traditionally used a lot lower AC current devices when caravan and camping than they do today.
Inverters were never intended to run air conditioners, microwaves , coffee machines and the like.....that is until lithium came into the RV market.
For low current devices (under 600W) it is fine to connect an inverter to your AGM battery system. AGM batteries can put out low current for a long period of time. When you need to go near 1000W or more , then you should consider a lithium battery.
You can connect an inverter to AGM batteries but you need a lot larger size batteries than lithium (to cope with the high current).
A general rule of thumb for AGM or GEL batteries is a 1000W inverter should be coupled with 2 x 120A batteries and a 2000W inverter will need 3 x 120Ah batteries.
Conversely, some 100Ah lithium batteries (Enerdrive, Invicta) can power a 1000W inverter and some 200Ah lithium batteries (Enerdrive) will power a 2000W inverter.