I can't speak for the glue brand you mentioned...I'm 100% certain that it is an excellent product...those folks have been in the scenery business for a long time...
however...over the years...(make that decades)...I have applied my fair share of sand, bird cage gravel, ground up leaves, yard dirt and dyed sawdust (plus glitter) with slightly diluted white glue...I like Elmer's Glue All at the present...but have used other brands...I use cheap brushes...and have never diluted to the level you mentioned in a spray bottle...
Howard