Agate is simply banded quartz, the same material as the majority of sand and gravel. Those look to be artificially coloured however, there are a lot of those about. I expect they would chemically/biologically be harmless, but would expect some of the vivid colours to fade over time.
A lot of geodes/crystal groups would be very bad in a freshwater tank. The commonest "crystals" you find are CaCO3 and will harden your water and raise your pH. If any of these crystals fizz when you drop acid, like vinegar for example on them, they have no place in a freshwater tank unless it is an African Rift Valley type set up where the high pH is an advantage rather then a problem.
Many others are heavy metal salt crystal, Cassiterite, Sphalerite, Blende, Pyrite, etc., these do not readily react with vinegar but are undesirable in the tank. If you run lower pH tanks, espeacially so.
The comment about sharp edges is very valid.