The game will still have all the free assets from the asset store, but the open source information will have a text file with links to the erased free assets. Your code and everything else will still be available to be seen in your open source.
I still need to try this, haven't done this in years. In theory, after you have created your final game. Go to where your game is stored in "Unity Games". Find your game and make a copy. Open the copy, it will look something like this:
Open the "Assets" file and find all the free assets from the Asset store and delete them.
Remember to create a text file with links to the free assets and add it to this file, zip it up and upload it for the game jam.
Hope this will work.
No, because you made a copy of the game, the copied file will become your open source file. You are uploading two different files, one is the game file with the free assets and the other is the open source file with the deleted assets.
The created game file with free assets looks like this:
You cannot see the asset file.