You should not need to worry if a capacitor can output enough current... they can provide a SCARY amount of current if they are allowed to.What happens to the current in this case? Does a fully charge capacitor even have enough current for when charging the battery despite using a boost converter?
The question here becomes:
-Can the Capacitor put out current 'long enough', to create an acceptable charge on the battery?
In a perfect device, a boost converter will take an input voltage and double it, but will also halve the input current... ie. 2.5V and 1000mA into the device, becomes 5V and 500mA leaving the device.
In reality, you end up loosing a little in the device, so you may only get 5V and 450mA out of the device.
A capacitor can almost be compared to a very tiny battery. The voltage will start out high, but will rapidly fall as you pull energy from it. The larger 'Farad' reading a capacitor has, the more charge it can hold at a time.
Think about filling a cup of water with drops of water. A smaller capacitor will be able to provide a much smaller drop than a large capacitor. It will take a LONG time to fill the cup, but you will eventually get it full. (This also depends on how many drops per second you are putting in) However, there is an issue. Batteries and Capacitors suffer from 'self-discharge'. Now pretend that cup has a very small pin-hole in it that the water leaks out. You notice that if the drips don't come in fast enough, the cup will remain empty.
The same principle applies here. A smaller capacitor will need to cycle much quicker than a large one to fill a battery to overcome losses. This would also mean that the left over energy in the capacitor would simply be added to instead of waiting for it to completely empty.