Impossible to say, without trying.
If you are lucky, then yes, you may be able to just open it, once you have enough space; but it is possible that the library may have become corrupted.
Usually the bulk of space is used by stuff that you don't even need - transcoded media and render files.
Now, these should normally be deleted from inside FCP, which may not be an option right now.
But if you can make some space and can open the library, then immediately do this: select the library in the browser sidebar, go to File->Delete Generated Library Files... and check all the options. Quit FCP and see how big the library is now, and much space you have regained.
And, if you haven't, do consider putting your media in an external SSD, and using not one big library, but one library per production.