Smaller fragments or old crumbled heat tee plastic. Will likely continue to break down into smaller and smaller bits. They'd not likely cause a blockage of flow, to point of resulting in noticeable ECT (engine coolant temp) increase.
But they can block radiators small tube and oil cooler passages. These would likely just be partial blockages, not stopping all flow.
The reason I always replace the first (short 90 degree) hose out of engine going into Tee. By removing hose from water out (hot) pipe coming up from water bypass and not pulling tee off the hose. Is if, plastic brittle (often), it often falls into engine side.
I cut this 90 degree hose off pipe, so that I don't put and undue force on the water pipe where it's pressed in water bypass joint. To much force on pipe, we'll get leak at joint.
I'm very careful to NOT score the pipe with my cutting tool, as I cut hose off.
That said:
Blowing out heater cores, is easy. Just disconnect hoses at TEE's, blow into or pump from firewall side and catch or suck from other end of firewall side. This isolate heater cores, bypass engine coolant side. Upper hose are front heat core, lower smaller hose are rear heater core. DS (BK1) is hot coming out engine, PS (BK2) is return to engine.
If blowing out with air or water, just don't create excessive pressure. Keep in mind, the sealed coolant system runs/flows at ~15PSI. So make sure as you blow out, to not restrict or cap catch end.
I like to catch coolant or distilled water, so I can inspect for contaminants like practice of tees.
Here I use a pump to back flush with distilled water. Sucking distilled water through heater core.
Here I'm blowing out core with HP air. I used 15PSI. Since out end open (no capped or restricted), moe pressure can be used.
Engine side not so easy. What I have found. Often these plastic piece will end up behind thermostat in water inlet. They come in from the water crossover pipe (return pipe on PS) into back of water pump. But they can and will travel through engine and end up in oil cooler (bracket holding oil filter), if not lodged first, in blocks water passages. But generally the pieces are small enough, they make their way to the oil cooler.
Two ways come to mind, to get out of oil cooler:
Remove oil cooler and clean out.
Or (just came up with this idea) remove hoses from each end, then backflush. Direction of flow is from back to front (side of BK 1 block to oil cooler, then up front of engine). I don't like introducing tap water, distilled is best. But if one didn't have a pump, to suck distilled water through back side of oil cooler (hard area to get to). One could blow out with garden hose, then blow oil cooler out with air. Then triple flush (engine running, coolant system sealed back up) coolant system, with distilled water. Air could be tried, but may need flow of water to dislodge.
Coolant flows out oil cooler, up front of engine.
Coolant come from block into back side of oil cooler
Oil cooler itself, is not hard to R&R. The hose clamp on back side is a PITA. Trick to make easy: Remove oil filter and hose from front, large center union bolt (oil filter thread onto) that holds oil cooler in, and then the rear hose clamp.
