Can multiple people create one multisignature address, while keeping their private keys private? Is it possible for person A, person B, and person C to create a multiple signature address without one person needing to initially know all three addresses to create that public address in the first place?

Ideally 5 people somehow create an address together, maybe passing it on to each other? But only if 3 out of those 5 private keys are used, can money be gotten out of that wallet?
You need the public addresses of all persons involved in order to create the multi-sig address. So if you are creating a 3 of 5 multi-sig address you need all 5 public address.  In order to retrieve funds from that address you need signatures from 3 of the 5 people (or however many signatures you require). Check out this example here, which was a huge help for me. 

bitrated.com and https://coinb.in/multisig/ have open source implementations of this as well.