I had one in my house in Texas. It was a beautiful carpet and the house was dry enough that the water issue wasn't a problem. The things to consider are...A how "wet" are you when you step out? I have long hair and tend to flip it into a towel before I step out of the shower (door open in the stall) so the heaviest water left on me is covered with the towel. So basically theres some drip but not much. Our shower also has a curb, so there's no residual splash water to consider. This was in a master bath, so no careless children running around dripping wet :) If your house is damp already though, you'd want to think about how long it will take for any drips to dry in the bath. If it's a very damp climate, a carpet could stay moist for some time and cause mold issues, but in most climate controlled homes, or in dry climates, it's a non issue. In houston you have to pick up your rugs or mats regularly anyhoo to ensure that evil buggies don't hide under there. I always hung it over the shower glass and let it dry completely, maybe once a week? We never had issues. If it's hand dyed (very pricy) you might want to test for water safeness. Some of them run badly when wet. But if it's a normal wool or mixed cotton/poly etc., it would probably be fine! By the way, I wouldn't tuck it right up to the sink. I'd push it back about 4" so that you have 4" on both the shower side and the sink side. If that makes sense. What's the worst thing that could happen? You could try it this week and if at the end of the week the thing is perpetually damp...it isn't a good idea so take up the carpet, let it dry and use it somewhere else :)

Do you have to use non-white bath mats or rugs? I'm in the middle of a bath remodel and just sealed the grout in my shower and will do the same in a few days to my floor which just went in yesterday. I would test your sealer on a sample tile to see what happens. I'm using 511 Impregnator and if it didn't change the color (darken) my grout, which I'm sure is more absorbent initially than your marble, I'm not sure how it would discolor it. But you have to test it. BTW, the 511 Impregnator was recommended by my tile guys and it ain't cheap ($34 for a quart). I don't know why you wouldn't seal the grout on your floor which will get wet and have dirt ground into it.

https://www.overstock.com/Bedding-Bath/Bath-Rugs-Bath-Mats/Round,/rug-size,/4527/cat.html?cid=243678&TRACK=PSGGL&gclid=EAIaIQobChMIt5zJg8n02wIVEVuGCh1rSQf4EAAYAiAAEgLmyfD_BwE&gclsrc=aw.ds&dclid=CKXb-YzJ9NsCFY63yAodwpwENA

I have a beautiful tile and marble shower with frameless glass doors - why would I want to drape a rug or a mat over it? I don't have a tub but again why would I want to drape anything over the side of the tub as part of the permanent decor? I am not sure why something on the floor is necessary. I had a rug prior to my remodel because I just assumed it was what was done. When I moved out during the remodel, a used towel on the floor served the dual purpose of absorbing any drips and providing a non slip surface when my wet feet exited - this was in the bathroom of death which had slick 12 x 12 marble tiles :-). After using a towel for six months I realized that having permanent or semi-permanent rugs/mats on the floor only created an additional thing to clean - cluttered up the visuals of my bathroom and served no purpose for me.