Yes, any data can be embedded in a blockchain using transaction metadata, and then all participants in the chain will then receive a copy of this data.

Having said that, blockchains only make sense for file sharing where it makes sense for every node to receive a copy of every file, and (at least in current implementations) every node keeps every file permanently. Otherwise you'll want something based on distributed hash tables, where files are stored with just a few copies and retrieved only on demand.