As a general thumb rule, if an item can roll with a random set of parts and a random set of annointments then it can have any combination within those 2 sets.
Annointments aren’t cancelled out by any item parts, the same way item parts doesn’t make certain annointments available. Sickle is a good example, it can’t roll with 160% splash annointment and the “boom” part which makes it a splash weapon doesn’t add it to the annointment pool, if that makes sense.
Quest rewards is were you’d see the most restrictions, with a “no exceptions” rule. Meaning "fixed parts [Yes/No] or, can be annointed [Yes/No].