Better, in my opinion, than globally turning off those messages is to turn
them off only when appropriate (by using DoCmd.SetWarnings False before
running the query, and DoCmd.SetWarnings True afterwards), or by using the
Execute method of the database or query to prevent them from being issued in
the first place.
I prefer the Execute method, since it also allows you to trap for errors,
should something go wrong during the append.
If you're using a SQL string, you can use the Database Execute method:
CurrentDb().Execute "INSERT INTO ...", dbFailOnError
If the query's been saved, you can use the QueryDef Execute method:
CurrentDb().QueryDefs("MySavedQuery").Execute dbFailOnError
Note that these are DAO methods. If you're using Access 2000 or 2002, you'll
need to make sure that you've added a reference to the DAO library, since
neither of those versions of Access included that library by default.