2008 PT Cruiser P0340 Misfire: Battery, Cam Sensor & OBD-II Code Diagnosis

My wife's 2008 PT Cruiser with a 2.4L naturally aspirated engine started exhibiting hesitation and bucking about two weeks ago. The vehicle did not stall, but the check engine light came on. After reading the OBD-II codes, I identified P0340 — which indicates a misfire related to the camshaft position sensor. I replaced the spark plugs and ignition wires, reset the system, and the car ran fine for a few days until today. This morning, the issue returned. The wife was concerned about driving it home and took care of it carefully. A new OBD-II scan revealed: P0340 (current fault), P0700 (pending fault indicating transmission control issues), and P0562 (historic code related to fuel pressure). I know the original battery is quite old, so I replaced it today. Additionally, I cleaned several ground connection points to ensure proper electrical flow. My question: Can a weak or aging battery cause intermittent electrical problems that trigger the check engine light? For example, could insufficient voltage affect the coil and spark plugs, leading to misfires? If the P034-than code returns, I suspect the camshaft position sensor may be faulty. If that were the case, would it typically flash the code continuously or only appear intermittently? I'm seeking input on whether the battery issue could be contributing, and what steps to take next for a proper diagnosis.