I made the game in Godot Engine. The exported game has refers to the PCK file in my user folder. However, when I downloaded it again it didn't know about the PCK file location and would not run. To fix the problem I had to embed the PCK file into the .exe itself.
So I just want to test and make sure something like that doesn't happen for Linux or Mac, just to be sure. But ideally I could do this after I release the game for Windows.
If you have static references to a local file, that is not good for a distribution file.
But again, merely downloading should not change a single bit here. If that uploaded file would have those static references to your specific user folder, downloading it would not change anything. There should not be any difference from you copying the distribution archive file to a new location vs. downloading the exact same file from Itch.
And you might want to be careful with godot packed exe files. Some of those do trigger virus warnings.
When shipping a Godot game for desktop, the .pck file belongs in the same folder as the .exe. That is where Godot will look for it by default.
You can go to my user page and look at the Windows version of "Ratsnek" - that's how things are supposed to be shipped.
On Windows and Linux, simply slapping the .pck and the executable (.exe on Windows, ELF binary on Linux) into a ZIP file and having the user extract both into the same location works fine. On macOS, both the .pkg and the executable will usually be bundled into a single app bundle.
If your Godot game loads any game assets from your user folder, you are doing something fundamentally wrong.
And to answer the original question: You can add Linux and macOS versions later but you have to test them BEFORE you upload them to itch.io, or as a separate, hidden product. When you add them to your existing, public project page, they will be shown to users by default.
Uploading and downloading your game files does not change their content at all. That means you do not need to upload your files to itch and redownload them to test them, but you should test them out on a clean machine or have a friend test them for you before going fully public with them, especially if you are doing nonstandard things with how you manage your files.