No. It is actually silicon dioxide. Agate is banded chalcedony. It is one form of microcrystalline Quartz. The crystal layers are microscopic and the structure makes them feel waxy. The different substances form under different environmental circumstances. Flint, chert, chalcedony, agate and more are all very hard, formed from silicon dioxide and have similar properties. They do not crack like other rocks. They fracture. The fractures are called conchoidal fractures. They look like divots. If you look at arrow and spear tips, you see these fractures that were chipped out by the flint knappers who preceded us.
Agates in particular are believed to be formed in pockets formed in lava by air bubbles. Cooling lava has air bubbles that occur as the lava forms into rhyolite and other volcanic rocks. The rock is porous. Over time water with silicon dioxide in solution seeps into the cavity and evaporates, leaving a layer of minerals behind. The process repeats, eventually filling the cavity. Voila, an agate.