Epson 3880 Mate ink
You can profile a mat paper using photo black ink and a photo paper media setting. It shouldn’t be a problem, but it won’t be optimal – the blacks will not be as black. That is why there is a mat black, to optimize dMax.
In the other direction: profiling a photo paper with a mat paper setting and mat black will work too, but you will have gloss differential problems. The areas where the mat black ink goes down will not be as glossy as the areas where the other colors are laid.
If you want to see how photo black looks on mat paper, just print on regular bond paper using a photo paper setting – I do this fairly often when I just need to print something like an invoice and don’t want to switch inks. Apart from it putting down more ink than you would want, it will look ok. Try a small image on photo paper using a mat paper media setting to see the gloss differential.
On a dye ink printer, you don’t have the gloss differential problems – the dye based ink soaks in and the surface of the paper retains its gloss. On a pigment ink printer, most of the ink is on the top and has a strong impact on the glossiness of the surface of the paper.