Yes you can, I've never had a problem adding it to the fermenter when need. It is in a sealed container after all.
I'm being overly cautious or paranoid.
Ding ding ding.....
It's mention in the instructions that it can be added to starters or the fermenter, millions of folks besides me do it all the time, with no issues.
I don't use the eyedropper as an anal probe or anything, just open up the bottle, squirt a dew drops in and the seal the bottle. I'm pretty sure it's gonna be fine.
We use cough medicine or malox from open bottles all the time and don't get food poisining from it, do we?
*shrug*