IME yes, enough transfers into breastmilk to make a difference in an EBF baby with a cold. Once DS started solids I had to give it directly to him, though, to make an impact on his colds.
I didn't notice SA reducing the number of illnesses DS got, it just reduced the severity and probably the duration. And the amount you'd need to take is highly individual--there are quite a few reasons it could be higher than what I've read is a typical amount--which is 50 mg/kg per day when healthy and 250 mg/kg per day when sick (both those amounts need to be spread throughout the day, 3-4 doses, not all at once). I'd consider those starting amounts and then start experimenting from there.