I have one last question for you:
Is it important for a charge controller to have discharging capability?
Why would I need that?
Is there anything wrong with charging a LiPoly battery that is still 50% charged?
One last question? I counted three.
The discharge function is used mainly to determine the actual usable capacity of a NiCd or NiMH battery pack, and can also be used to improve the capacity of NiCd and NiMH packs, which can suffer from so called memory effect if they are only partially discharged each time.
This function is not generally used with LiPo packs which do not suffer from this memory effect, so it would just be a complete waste of an otherwise usable discharge cycle of the battery.
If a fully charged pack is not going to be used for a long time, it is suggested that it may be beneficial to discharge the battery to a reduced level
(usually 3.85V per cell for LiPo packs) and this is probably the only time you would want to use a discharge facility.
Without the discharge capability, you could just use the bike until the battery had been run down to the required voltage instead.
The Lithium battery prefers a partial rather than a full discharged. Frequent full discharges should be avoided if possible. Instead, charge the battery more often or use a larger battery
So charging a LiPoly battery that is still 50% charged will be much better for the battery.
Most of my rides are usually around 3-4 miles long, which uses less than 20% of my battery's capacity, and I always charge it fully after each ride.
I hope this answers your question(s).
AlanP.S.
In case you hadn't realised, the charger you have in mind requires a separate power source. Although it can be powered from a car battery, a mains powered voltage supply of between 11 and 18 Volts and at least 5Amps might be better.
(The +12V output from an old PC power supply should be ideal)