Process Recipe and ICC Profiles

To print I save a 16 bit TIFF using the Adobe RGB ICC profile. The software I use to print allows me to select the paper profile I am using. My questions is, is there any advantage to selecting the ICC paper profile before running the process recipe and saving to a TIFF? For example, if I know I am going to use a matte paper, is there an advantage to using that paper’s profile rather than Adobe RGB?

Thanks.