If the couple invite you too, sure. If not, I would say not. I would rather guests took home the flowers from my wedding than have them thrown away but as a guest I wouldn't take them unless invited to.
normally, it is part of the understanding that centerpieces can be taken, but asking can never hurt. I remember attending a wedding where the centerpiece was a beautiful bouquet resting in a vase which had a fish in it (the vase served as fish bowl as well). I took the fishbowl and had wonderful memories of the wedding associated with it for many months afterwards. Again: no harm in asking.
I've heard of people having fish in vases on each table meant to be taken home by guests as gifts like you might have bonbonieres (ie. one per guest). I really dislike that idea because getting a pet is a decision that needs to be thought through properly and you need to have the inclination, the time and the knowledge to look after it properly. This goes for fish as well as furry pets. The fish were in tiny vases (I don't know the size of your fish bowl, hopefully it was a bit more generous), and though they were bettas (Siamese fighting fish) which people think should be kept in tiny containers, while the fish can survive under those conditions it really isn't the best life for them to have. A puppy could survive shut in a cupboard but that doesn't mean it wouldn't be kinder to let it out to run around. I have even heard of people keeping bettas in vases with flowers under the impression that you didn't have to feed them because they would just nibble on the plant. Bettas are carnivores, so they while they will nibble on a plant out of desperation if nothing else is available they will slowly starve to death if given no other food.
All in all I really think animals should not be used as decorations, at weddings or anywhere else. They are living creatures with rights.
I think if the couple invite the guests to take home the flowers, than that's totally ok, right? So long as individual guests don't start smuggling out bags of centre pieces (unless previously arranged to do so), I think you're probably all good.. Such a waste to just leave those beautiful creations all alone.