Direct quote from the Canon New F-1 manual (paragraph excerpt):
There are several shutter speeds available with the New Canon F-1 even if the battery fails. In this case, remove the battery from the battery chamber.
Then below the paragraph in a highlighted box:
The camera will not operate if you leave the exhausted battery in the battery chamber.
--So yes, it doesn't matter if the battery is in or not- IF the battery is not exhausted.