If the Perf Manual states a DH it can be used. If it doesn't it can't. Good point about varying terrain and DH..MAN 06L is a good example..where you can't do a Cat2 or Cat1R approach but can do a Cat3b approach (due to the Bollin Valley)...but the Perf Manual should include notes if this is a known problem.
Can't think of any non-precision approaches that have a DH but expect somebody could prove me wrong!