Contact your municipal water supplier and ask if they disinfect with "chlorine" or "chloramines". Sometimes, they use both or switch seasonally. As others have indicated...if they use ONLY chlorine, then your drip system will allow this gas to dissipate and the scenario you describe should be ok. If they use chloramines, this will not dissipate into the air and you will eventually accumulate a concentration which is toxic to both, the bacteria and your fish.
If you must use the system you describe and your water DOES contain chloramines, you can probably blunt the effect by doing the following:
1. Calculate how much fresh water is added to your tank by the drip sysytem within a 24 hour period.
2. Every evening or morning, add a corresponding amount of dechlorinator, plus maybe 10-20% extra. This will be in the tank, waiting to bind with the incoming chloramines. Use a dechlorinator which does NOT bind to ammonia or nitrites. What I don't know is how effectively these dechlorinators are removed by activated carbon. If the dechlorinator binds readily to carbon, then all bets are off. If you don't use carbon, then you're in business.
This approach is certainly not perfect, but should offer some additional protection.