The RTC will not draw any current from the battery when the board is powered up. The RTC draws 2uA current and the voltage regulator draws about 10uA. The battery should last for at least 7 months without power up.
Well let's calculate: 0.035 Ah / 0.000012 A = ~2917h -> 122 days -> ~4months. Or what am I missing?
UPDATE: I've picked one of my GESBC-9260 and measured the current: it is about 6.1uA (@2.5V). So, a 35mAh battery should last about:
0.035 Ah / 6.1 uA = ~7.9 months