I have an .esp that does nothing but override pre-existing FormIDs from Skyrim.esp. I'm trying to use GetFormFromFile in an additional mod to check if the first one is loaded, but it doesn't seem to work on FormID overrides.

Is there any solution?

You'll need to insert a dummy form in your plugin that belongs to it. If all you have are overrides for 00 forms from Skyrim.esm, your mod won't be recognized as being where they come from.

Use your dummy form for the GetFormFromFile check in the second mod.