So wait.. are you saying the charging circuit will not charge it to full capacity? I'm confused..
No, hypothetically the opposite: It will charge the higher capacity battery to a bit higher capacity than nominal, the difference in the charge percentage is really small.
Plus (a bit counterintuitive, but result from how the charging really works) if the original battery was fully charged after 2 hours, with double battery capacity the full charge time will be just about 3 hours (not 4).
How the charging works:
The charger is a "simple" (but accurate) voltage source with a build in current limit for bulk charging and a current comparator to determine the end of charging.
Plus it contains an undervoltage comparator, which reduces the charging current limit to ~CA/10 when the voltage is too low (below about 2.7V), to prevent high current charging of a defective cell, so prevent the eventual fire.
Initially with a depleted battery, the battery voltage is low (but assume it is not overdischarged, so still above 2.7V), so the charging circuit delivers full current (typically in the range of 0.5..1CA).
During that time the cell voltage gradually rises. This is called "constant current" mode, or a "bulk charging", with 1CA current limit it delivers about 80% of the rated capacity.
Once it reaches 4.2V, the charging circuit maintains that 4.2V, so the charging current starts to decrease. This is called "constant voltage" mode, or a "topping off", it delivers the remaining charge. But because the current drops down, the charge delivery gets slower and slower, so it take usually another hour to deliver the last ~20% of the charge.
If you keep it like that, the charging current will in the "infinite" time approach the selfdischarge current and so the charging turn over into a a kind of maintenance charging.
Te problem is, time spent at the high voltage state causes the cell to degrade over time (effect starts above 3.9V, it depends exponentially on voltage and temperature), so permanent maintenance wears the cells pretty fast (compare to other cell states), therefore it is beneficial to somehow detect, when there is not any practical capacity to gain from the prolonged charging and so switch the charger OFF.
For that purpose most cell makers recommend to monitor the current and switch the charger off once it drops down to 5..10% CA.
Now what happens when you use double capacity cell compare to what the thing is designed for:
If the original has 200mAh battery, the charger will be set to 200mA current limitation for the constant current mode and about 20mA charge termination threshold. And that remains regardless what size cell you put in.
With a 200mAh cell the first 80% capacity would be delivered within a hour, the next hour will the charger spent in the constant volt mode till the charging current drops to the 20mA threshold, to declare the cell fully charged and switch the charging off completely.
If you connect a 400mAh cell, the 200mA will take double time to reach the same 80% charge as the smaller cell reached after one hour. But because the larger cell has most likely half the internal resistance, the voltage is not yet at 4.2V, so the charger continues delivering the 200mA for few extra minutes, so delivering more charge at the same pace.
After that in the CV mode the charging slows down, but because with the bigger cell we are already further in the charging percentage and the battery internal resistance is lower, the current drops faster. At the moment the current drops down to 40mA (10% of a 400mAh), the cell becomes fully charged.
But because the end of charge threshold remains the same 20mA, it is just 5%CA of the larger cell, so it take some extra charging to reach that shut off point, that is the extra charge you get (on top of the double main capacity). But in the real life this difference is negligible - such difference gets "drowned" into the production tolerance of the batteries and the effect the charger voltage tolerance has for the same.
Someone may argue the extra charge means extra wear (even when very minimal). Well, could be when acting alone, but the lower bulk charging current (relative to the cell size) means less wear (mainly thermal) during that part of the charging and that would completely offset the extra charge influence. So again, the other factors (manufacturing quality, the exact used chemistry and internal construction, CV voltage accuracy and use pattern) will influence the cell life way more than the charger current levels do.
