In short, no, they are not always compatible.
I have had photo papers (Kodak I think) that actually rejected Epson pigment (Ultrachrome) inks (it sat on the surface and refused to dry properly.
I have also seen certain dye inks leech under the surface of glossy photo papers leaving (in one case) a magenta halo.
Pigment inks tend to leave a matte finish on glossy papers, but work well on matte papers as they dont soak in and bleed (they dry in the surface), whereas dye inks tend to leave a super glossy finish on glossy papers, but a flat, dull finish on matte papers.
The only way to know for sure is to test, luckily most manufacturers do tester packs so you dont have to potentially waste £20, £30+ on a pack.