All pearls can get wet. Josh wore his Tahitian on a string in surf and sun for years, with no damage to the pearl.
Wait, I take that back for cheap or overtreated akoyas. They shouldn't get wet again. Good, untreated akoyas like water too.
The first thing is the silk makes it impractical to wear pearls while in the shower; they stretch out quickly if you get the silk wet, so cleaning them would depend on the damp cloth and an occasional washing with special care for the silk, until it is dry. Under these conditions, the patina may not improve except when the pearls are restrung.
On the other hand, man-made nylon polyester threads coming in several forms don't stretch when wet, so your pearls can be worn in the shower. And will shine up well, even though worn 24/7.
I have recorded here, in other threads, my experience with wearing a cultured freshwater pearl (CFWP) bracelet for over a year, in and out of the water 24/7. It was to test the synthetic thread, so I used commercial grade beading pearls with wrinkly skins. The surprise was that the patina/luster got better, if anything. I am now wearing a Sea of Cortez (they are untreated) pearl bracelet strung on silver wire, 24/7. I am sure it will fare extremely well as the nacre is thick.
In my opinion, stringing on silk, sucks. It prevents the full use of the pearls for 24/7 users. It also prevents truly cleaning the pearls with the water from the shower spout on them and the mild shampoo that drips down on them from washing your hair.
I don't use perfume or spray scents on my neck, ever. That would hurt the pearls, even after the products are dry. Even the slightest amount of any kind of spray on the neck is not good for the pearls. If you get at all warm, say to the point of sweating, the acids from the perfumes or spray products that fell on your neck, rub on the pearls. (Unperfumed skin moisterizers/sunscreens seem fine, but the pearls still need cleaning)
In my opinion, even if you use silk thread, you should wash the pearls often, even use an actual pearl product to do it. The damp cloth isn't good enough if you sweated, esp. with spray perfume on your neck. The damp cloth doesn't clean up around the holes, where any acid build-up will begin to break down the nacre where it is thinnest.
Grandmas' akoyas often attest to the above. Funny thing, it isn't the exposed oft rubbed surfaces of the fat part of the pearls that tend to chip first, it is around the drill holes where the grunge builds up.