There's no specific way to tell if the lot is full, but of the dozen or so times I've been there I've never found it fully at capacity. Last time I was there (a year or so ago) it was a dirt lot with quite a bit of space off to the north if needed.
If there's truly no parking there (granted, I've never had this issue or heard of anyone having the issue, but just in case) the commuter bus station a couple miles down has parking for up to 7 days in a part of their lot, and in the past the Holiday Inn on the west side of town has allowed overnight parking for non-guests (though call ahead to confirm.) I wouldn't worry about it, though, as I'm not aware of parking being an issue at the Amtrak station itself.