I'm sorry for laughing, but, I just can't imagine the trouble I'd be in with daily deadheading compulsions!
I have a relatively newish Mme Alfred Carriere, and I do not struggle to remember the fragrance or the relatively fewer thorns, but, I cannot recall if it seemed to self-clean or not...I'll have to pay more attention next year.
I've got mine in a big spot that I cleared between a tree and a fence and some ~ 6' shrubs--
It is poised to fill its spot soon and I was very impressed with it last year (2nd yr), so hoping next year will be even better.
Anyway, it's a
great rose and I hope someone comes along who can answer your question.