I need to have a query that will query the SharePoint database (or if it is
possible, do this in SharePoint somehow) so that I can tell any users who do
not have a specific profile property assigned to them.

For example, looking at the PropertyList table I see that my custom property
has a PropertyID of 10001. Now when I look in the table UserProfileValue I
get a listing of RecordID's (which correspond with the RecordID of the
UserProfile_Full table that has the actual users name) and multiple
PropertyID's associated with each RecordID. Such that each user can have
multiple properties. I am looking for users who do not have a PropertyID of
10001 listed.

I am not an expert at SQL queries and have found this hard to write. Anyone
have any ideas?