Depends on the use, battery size, and charger size, partly.
If it is cycling less than maybe 12(?) times per hour at the worst, and the battery charger is reasonably suited to the battery size (not a 20A charger on 7AH batteries), probably all is good.
Personally, I do not like to take the batteries below about 12.2V on a 12V system, regardless of lead-acid battery type (flooded, SLA, gel, AGM).
Naturally if the load is vital I would not have a problem taking the battery a lot lower.
If the load is large compared to the battery capacity, the voltage will "Bounce back up" without any charging.
Could take the battery lower in this case, maybe 12.1V?
A small battery capacity and large load will cause the charger to cycle pretty fast, as in maybe once every minute or 2.
Once every minute or 2 will not hurt anything, but it means something in the system is too big or too small.
(I have to say those are nice answers you gave, thanks)
G-