My question is moreso if I were to somehow make a blockchain that instead of exchanging bitcoins exchanged files. Would that mean that in that network, once that file is sent to another party, that I no longer have access to said file (assuming that I have not copied it)?
The blockchain doesn't store bitcoins. It stores the transactions that exchange them. Imagine all the bank statements in the world. That's what the blockchain contains. Like making a photocopy of your bank statement won't make you richer, copying the blockchain has no effect on bitcoin allocation.
A file on the other hand is quite different. Copying it duplicates the information.