I AM NOT A DR, THIS IS JUST MY EXPERIENCE!!
So, yes, my sweet little Rho could sniff out, find, and chew up that type of ribbon in an instant! It happened many times before I put my foot down and said, "NO MORE RIBBON IN THE HOUSE!!"
It never seemed to upset his stomach for more than a couple days, but it did take a couple days for it to come out. In the mean time, his bathroom and eating habits were still pretty normal. He would sometimes puke up a bit of food before the ribbon came out, which was pretty normal for him weather it was a hairball or somthing he shouldn't have eaten - it was like a clue to me that I'd soon find a hairball or puke-ball of some kind soon.
Personally, I never took him in for ingesting something like this. He always ate and drank well, was never unusually lethargic, so I didn't see the need. However, I know that when cats ingest strings it can get dangerous fast. If I were you, I'd keep and eye on Beenie, but try not to worry.
One time, I did not realize that Rho had chewed the rubbery string out of one of my shirts - you know, the kind that are sewn into the shoulders you're supposed to hang the shirt on so it doesn't get stretched? Well, one day he was scooting around weird on the floor because half of the string was hanging out his butt. After that, I always cut those strings out!!