Absolutely possible. and actually common.
The only problem is this...... what have you got?
E coli?
Salmonella?
Corona?
or any of the other dozen or so possiblities?
Always, always use super clean, sanitized items from calf to calf, and also yourself!
We wash and, or sanitize between calves, never share anything, and always clean ourselves with hot water, soap, and sanitizing gel.
We also use alot of bleach when cleaning up the bottles, nipples, buckets, balling guns, etc.
Always assume that your hands etc are contaminated when you come away from the calves. We start using disposable latex gloves when we have to deal with sick calves as well, sure makes things easier.
But don't beat yourself up over it, it can happen easily, and has happened to me years ago, not fun, but an unpleasant reminder that we need to keep diligent about sanitation.
Good luck!