Will checking the backup voltage on an RTC drain it's backup battery?
You will certainly drain the battery through the resistor. The amount of current you will draw will be governed by Ohm's law: I = V / R. Lets say your battery voltage is 3V (i.e. the usual chronodot Vbat). With a 4.7 kOhm resistor you will draw 3/4700 = 638 microamps continuously. If you make that a 1 MOhm resistor, you will instead draw 3/1000000 = 3 microamps. And If you make that a 10 MOhm resistor, you will instead draw 3 / 1e7 = 300 nanoamps. 

The bigger the value resistor your choose, the less current you will draw continuously, but the longer it will take for your digital pin to transition (think R*C time constant governed by resistance and the capacitance of the pins and traces). So long as you wait long enough (or check back periodically) after startup, you should be OK with a 10 MOhm resistor. Theoretically, you could pick up more noise with a larger value as well (as it starts to look more and more like an open circuit), but I think you'll be fine. I might even consider going up to 100 MOhm.

A typical CR1632 has 130 milliamp-hours (mAh) of energy stored in it, and maybe 80% of that is useful life, so lets just call it 100 mAh for ease of calculation. A coarse estimate of your battery life is then milliamp-hours / milliamps draw. 


With your 4.7 kOhm resistor that's 100 / .638 = 156 hours = 6.5 days
With a 1 MOhm resistor that's 100 / 0.003 = 33333 hours = 3.8 years
With a 10 MOhm resistor that's 100 / 0.0003 = 333333 hours = 38 years


These are upper bound numbers that assume the rest of your system draws no power. They represent the lifetime of your system when it is off and the battery is simply drained through the resistance. There are also lots of second order effects that are not taken into account (voltage decay, internal battery leakage chemistry, etc). The resistor is unlikely to be your biggest problem depending on the lifetime you are hoping to achieve.