Letterpress ink is transparent and must be printed on uncoated cotton paper (or handmade paper from 100% cotton scraps). This results in light absorption. With metallics, there are little flecks that reflect sunlight, creating the shiny effect we are familiar with.
While there are metallic ink colors available, it will not be nearly as shiny as other methods such as foil printing or thermography. Gold letterpress ink in particular tends to have a green undertone.
If you have your heart set on a shiny metallic element, we can always look in to outsourcing foil printing. Another option is calligraphy with metallic ink - I am, after all, a calligrapher! We could print all elements on the press except for the couple's names, which could be hand calligraphed on each page.
With so many different printing options available, it's possible to dream up nearly anything!