The capacitor idea is NOT silly IMHO. It allows you to use a large voltage divider to prevent battery drain. 1M is perfectly fine. I am using 2 x 1M to measure a 6..8V battery. Response time is usually not an issue with a battery.
Of course you are right with the missing ground connection.
The capacitor idea is NOT silly IMHO
As already stated, a capacitor is nothing more than an energy storage device. Once it has charged, that energy has been removed from the battery and is no longer available for anything else. You still have to "pay" for that energy . It is not free. The amount of energy removed from the battery by the cap is more than the 160 nA that the analog input draws so the cap accomplishes nothing. If you use two 470 k resistors for the voltage divider, the total resistance across the battery is 940 k. If you had a 3.7v battery, the drain would 3.9 uA. That is 1/254th of 1 mA so an 1100 mAh battery would last
1100 mAh/3.936170 uA would last 279459.459 hours.
1.1Ah /3.9361702127659574468085106382979e-6 A =279459.45 hours.
279459.45 hours/24 hours = 11644.14375 days
11644.14375 days /365 days = 31.901763 years.
So how silly it that to use a cap to avoid a current drain that would 31.9 years to drain the battery ?