If you leave ANY flooded cell battery at 12.3 volts for a long period of time, it'll sulfate and lose some AH capacity. AGMs are flooded cell batteries. 12.3 volts is roughly 60% SOC, and there's absolutely no problem discharging an AGM battery that low, or even a lot lower. Just don't let it sit there if you do. Charge it back to 100% as soon as possible and it'll last for years.
AGMs are definitely NOT flooded cells, but they are still lead acid batteries. Any lead acid battery left too long in a discharged state will lose capacity. Maybe even all of its capacity. Always re-charge a lead acid battery as soon as possible.
Broadly speaking, AGM batteries handle deeper discharge rates better than flooded cell batteries - I believe the spec is AGM can gracefully handle 80% discharge rates whereas flooded wants to be limited to 50%. As Gary notes, neither will give a long life if left at a low state of charge, but the AGM handles deeper discharges and faster recharges more gracefully.
One thing to bear in mind is that AGM batteries have a lower specific energy than flooded cell and they have inferior temperature tolerances. Some pros, some cons. Kinda gotta weigh the whole cost vs. maintenance vs. limitations equation to see if AGM is an improvement for your situation or not.