I can't give any medical advice, but I have the same thing with Wilbur. He has eaten (and swallowed) so much crap I can't even begin to tell you - plastic lattice work, pieces of the compost bin, kilos of wood and sticks, stuffing/fluff...he is like a vacuum, he sucks it all up before I even realize. He even eats dirt. Plain dirt, and then he comes in the house and throws up a messy mud pile. The plastic lattice was awful - it is white and lines the garden. With all the snow, I literally didn't even know he has been chewing and eating it all winter. I feel terrible. Layla spits everything out, but Wilbur swallows.
Wilbur will throw up sometimes, and sometimes I can see all the things he has eaten. He poops it out sometimes too.
I try not to worry too much and I watch him constantly (number one priority is Wilbur-proofing the yard this spring). I would worry if I felt that he ate anything sharp (was the plastic Remy ate sharp? with edges?) - I have read tragic stories of EBs where something sharp perforated their intestine or something like that. I also try to remind myself that dogs have extremely powerful digestive systems, and should be ok with vegetative matter (I hope?)
I don't know how much this is true, but a friend of mine had to take her dog (shepherd mix) to the emerg vet because she ate a sock and some tupperware (!). Luckily there was no blockage (Kona must have thrown it up outside or something), and the vet told her that a way to tell if there is a blockage (other than days later when there is no poop and vomiting) is to lay the dog on his side and feel for distended belly and listen for gurgling (digestion noises). No gurgling could indicate a blockage, so you always want to hear gurgling. So I don't know how accurate or true that is, but apparently the emerg vet told her this.
Again I am by no means a vet and always trust your gut, if you are worried get him to a vet of course.
I hope some more experienced people comment soon, and I hope Remy is perfectly ok!