There should be no harm in adding water to your radiator. Winter is over so the chance of freezing the block is pretty much gone.
The other place you might be losing coolant is through the head gasket. Hopefully, that is not the case. Another is through the heater core and the water pump.
Since you seem to be up for a cooling system redo, consider a new water pump, thermostat, new hoses and perhaps a new radiator. These radiators break easily at the neck so be careful with that. I just ordered a new water pump and hoses, t-stat etc from BMA (www.bmaparts.com - ask for Patrick or Yves). The water pump was only $39.
Mike Holbrook
Meridian, Idaho
1992 535im, 17", Euro M5 Throwing Stars 8's & 9's, FK-451 235/45s & 255/40s, M5 Sway Bars 25/20, Conforti chip, Lowes Ram Air, glass sunroof