I found this Philips MES-232, but it says that I need to connect a 'filter coil' to one side. While I was harvesting it from the fixture, there were extra wires connected to the filter coil pins, that were cut off (I suspect it was mounted somewhere else). What is it, and can I run it without the coil?

This looks like power factor correction filter, if tgat is the case, the ballast will run without, just with lower power factor (because of the higher current harmonic content).