What does Balance Current drain means on the charger?

And what should the minimum be on the charger to be used by off-road track to s4 batteries, and races..
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It's the current the charger applies to independent cells of the pack in order to balance the cells all together. Usually it's set to around 200mA.

Are the batteries charged up faster if it is 350 instead of 200?

It's the drain current that the balancer cct applies to keep the cells of the entire battery pack near the same. The main charge leads are what source the large current to the battery (from the charger), but each cell of the battery will charge at slightly different rates, so the drain current tries to draw some of the current back out of the battery to keep the cells roughly at the same voltage. It might be slightly faster at balancing.

If the pack is significantly out of balance then yes a higher drain current allows faster charging. If/when the drain current is not sufficient the charge rate is reduced.

Some of the better higher current drain chargers charge faster even with balanced packs, they appear to take better advantage of the more accurate balance connection voltage readings, compensating for the slight voltage drop over the main charge wires and can charge a little quicker.